Most def got better at mixing. I think it depends on how you do the training. As of recently, I have been taking my sweet time playing these games. When I first started I was just going through the motion and just playing the game. That was beneficial and I could tell that it improve my ear for music production as a whole. I would say that just purely playing these games on a repetitive basis will improve anyone mixing skills to an extent because you are practicing even if you're not giving your full effort.
Now I am at a point where I sit and listen to the sounds very carefully I switch between the options. I do not play the games just to get my reps in purely as I did before. I used to be like "oh man did not do so well on eq knight today better luck next time." But I would never really look at my mistakes and try and understand why I got it wrong. Now I am trying to correct myself in real-time and understand what exactly I am getting wrong. For example, I just got done doing eq knight and one of the boosts was around 500hz. Before even switching between the two options I asked myself, "what does a boost at 500hz cause? What will be altered due to a 500hz boost? What is supposed to happen in the 500hz range, to begin with? I know that a 500hz boost can create muddiness, I know the 500hz range is considered the lower mid (the body) and I know that means the body of the sound will be changed. Then I switch over between the two option I listen to them and keep in mind what I am supposed to be listening for. I will then decide on what I think is right HOWEVER, I will listen to the other sound and ask myself "Well if this isn't the answer then what is the eq of this sound then" and I will spend a few seconds guessing what cut or boost the other sound is. I do that so I can clearly understand what I am doing, I do not want to be just right I want to know what made the other answer wrong too. It is why I wish sound gym would show you what the other eq of the sound is even if you get it right just so you know what you were listening to.
I think what I am trying to say is this will help only as much as you put effort into it. If you just play the games going through the motion instead of sitting there and really understanding what is going on then I think you're selling yourself short (not saying you are just in general lol).

I'm always learning something new here & in mixing.

This stuff is like karate practice. You get your fundamentals down so that your subconscious can take over in a tournament setting. Doesn't excuse tournament experience though, you'll learn that the hard way through recalls

I don't do 'real' mixing, I mean as a job or in the proccess of creating tracks with commercial perspective. And I believe, at my age, I won't ever have the chance, but as a music lover and amateur musician, composer and, well, mixer, I find SoundGym exercises very useful for effectively developing ear skills towards everything related to music. But it takes effort and an analytic approach to each game, as @Avery Anderson says, to achieve a deep learning of what's going on.

I think it is more like going to the gym...at the beginning you get a bit stronger, fitter, but as you progress you just get better at those specific lifting exercises - yes you are in general, fitter state, but when you go out in the real world and let's say you have to pack/unpack a truck full of boxes and furniture, you'd realise that you did not train for that - boxes don't have handlebars, ... (but maybe you were a little bit worse off had you not gone to the gym regularly) - But look at furniture movers - how easy they do it and it is not just because they are much stronger than a regular gym-goer - it is that they have experience and technique in lifting furniture and big boxes, loading trucks etc...

I think it helps, but is only one piece of the puzzle.
I see it in much the same way that I view musical tone ear training. We learn to hear scales, intervals, chords, progressions, and so on. Those things on their own are just theoretical, but it you learn them well, they will start to influence the way you play and what you can do as a musician.
So I would say yes, these games to make you a better engineer, especially because your ears are your most important tool. But there is an important caveat, ear training can only make you a better musician/mixer if you are actually doing music or mixing. If one is doing the activity that sound gym is designed for, I think it has great benefit. If you have the technical know-how to act upon the new information that your ears are fashioning you with, I think better mixes are very likely and also more repeatable. If you don't, then obviously there needs to be some study and application before the whole package comes together.

Hoping it's similar to the way music interval ear training can help you get better at playing along with a song by ear or improvising.

I think it's kind of all mentioned above already, but here are my 2 cents. :)
I have noticed that my overall listening skills improved by doing these games. When I opened some of my old projects, I immediately heard some bothering parts in a mix or even unbalanced synth-layers that I hadn't had noticed before. Just this week I noticed some very subtle but unwanted distortion while reviewing a song of a friend of mine. I'd like to believe these things are a result of the training.
If it really improves the mixing itself, is probably not just up to these games alone. But it only seems logic to me that better listening skills result in faster recognition of problem areas in a mix.

Been doing sound gym for ~2 months and last week I could hear an imbalance in my high hats at like 9k. I heard it, recognized the frequency and tamed it. I am still thinking about that moment. I never listen up that high and focus my time on the lows. This is a for sure a result of sound gym.

It's definitely making me better at hearing frequencies, levels and processing. After a few months hitting the Gym I'm much less trial-and-error with my mixdowns. I'm getting them done more quickly and better, which is great since I felt like mixing was taking time away from my actual music creation.
What it doesn't help as much with is the actual application of the tools in the context of a full mix. Like being able to actually identify and make decisions on level or frequency imbalances, the need for compression, reverb, etc. I guess this is harder to teach with online games and so much of it is relative to the specific track, style, personal preferences... I guess a lot of it is just down to experience and I'm sure collaboration/mentoring would help a lot on this front too. (also I'm currently revisiting the example mixes in Roey Izhaki's Mixing Audio book and feel I'm learning a lot!). But no doubt the ear training aspect is a great foundation for all this.
disclaimer: I'm only experienced with the "Gym" part of the site, maybe the other challenges help more!

I thinks it helps ,but after I reach 200000 SPI I will spend 90% time on practising mixing. practising mixing itself helps ear training in kind of more deeply. for example i was obsessed with peak master but after a certain point its not only the important that you know which sound is which frequency,but also should be able to hear like 1-2db boast. that made me consider eq night is more important after peak master. also mixing techniques such as fixing clashing frequencies, correcting phase issues, compression etc need to improve.

definitely getting better at mixing since I played much soundgym. I really hear the minor differences while mixing that i never hear before. And I talk about half a year ago..it especially helped me with hearing compression

They also, in general, make you more "aware" if that makes sense ;)

You definitly get better at hearing small changes, but not really for mixing. What i decided to do was to become more musical by doing ear training with notes, like intervas, chords, etc. The more musical you become the better desicion you will make to make music sound better.

Better at mixing because you will more clearly hear a poor mixing decision/have the ears to determine what most accurately aligns with your creative vision
I just got diamond ears and still feel like a whelp in the presence of people who have been mastering for a long time. I think ear training is indispensable

Fine listening skill helps to create great mix but if there’s no right direction for mixing, it doesn’t do nothing. IME, I became able to make better decision by training of soundgym. Still need training more though.