The more I thought about this question (
@FAST6191 : a very good one, btw
), the more I had problems coming up with things. The reason: I think the question is worded wrong. It should more be in the area of "what kind of skills AREN'T learned or honored due to video games?". I honestly believe that if you design a game well, you can teach just about any mental skill as well as a few physical ones. Or perhaps better said vice versa: you can design a game around A LOT of skills.
And to be honest, I'm rather disappointed by quite some responses here. On one hand, we identify very strongly with our hobby (we call ourselves "gamers"...you think people reading books call themselves bookers, or others moviegoers?), but on the other hand we apparently downplay whatever benefit we get from playing games. I honestly hope this is a kind of modesty on our behalf, or perhaps an inability to see the cause of certain of our skills. Because the opposite is also possible: that we just play the wrong games, or play the games wrong (not all games train the same skill. And like sports, you need to play at, or slighly above, your skill level to improve).
So...here's what I had written down before I thought "screw it" and gave the honest answer (which boils down to "almost everything").:
* English: at least this one is mentioned a lot. Perhaps as a Belgian, I see the consequences of this more often. Belgium is bilingual (Dutch and French). And for about ten years, I've worked directly with French colleagues. While that obviously has improved, my skill level is far from my English, which is like a second nature to me even though I hardly had to use it in any professional setting whatsoever (note: this is partially due to movies as well...we don't dub Hollywood movies but give subtitles)
* writing: this is perhaps a bit weird because aside from some text adventures when I was very young (Leisure suit larry(1) and king's quest 2) I never really wrote that much. But games gave me a good reason to communicate on forums. You always have topics, I've got an audience that can appreciate my humour and I just like to do it. The main difference between writing on forums and making essays at school is that the topics at school are made by someone who aims it to be as boring as possible.
* typing: I once followed a 10-finger typing lesson, but while that layed the groundwork, the actual practice is something I got from writing...and from playing cook, serve, delicious (oh, and a few others, like typing of the dead and epistory)
* guitar: no, not guitar hero...rocksmith 2014. I swear: if that game was available 10 years earlier and I had played it then instead of UT2004, I'd be good enough to be in a band. Unfortunately, I'm now "just" good enough to not be embarrassingly bad (which is still one step above, well...embarrassingly bad
).
* hand-eye co-ordination: a given for any avid FPS playing fan. It's just a skill that doesn't have much real-life use. I mean...a couple days ago I wanted to pick something from a bathroom cabinet when a plastic cup suddenly fell out (from about eye-level height of me). I just grabbed it before it could hit the sink. Now I don't claim that I could pull this off every time, but it's noticeable. Especially in my next skill...
* management (under pressure): from the replies, I notice that simulation games aren't that popular on gbatemp. But how to attribute resources isn't just interesting if you're an actual manager. Households or time are also things that can (and must) be managed. The 'under pressure' is between brackets because they're IMHO the main difference between RTS'es and simulation. The pressure is good when deadlines are tight, but simulations allow for more creativity or exploration.
* navigation: admitted: I'm old enough to still have had plenty of experience actually having to read maps to get somewhere. But even so, I'm among the best (if not the best) card readers among the people I've met.
* karate: this is my other hobby, but they influence each other a lot. Of course I know some posters will frown at this because they totally draw the wrong conclusion (yes, I KNOW you can't learn karate by playing video games. If you're just going to be captain obvious, don't bother replying), but that doesn't make it less valid. Why? Because karate utilizes a lot of other skills like reflexes, timing, effort, muscle memory and so on. How to act or react depends a lot on what your opponent is doing, and this creates a lot of "win" or "lose" states (eg if we practice defense against (slow) strikes at the head, the defense must be solid or it won't last if it was performed harder and/or faster).
* learning: yeah...the previous is basically a "I can use games for everything". And that's more true than not. I'll give stone age as an example: it's a worker placement board game I play with my girlfriend. Even though we only play it with each other (not entirely true: she plays the app version more often) and are both still new to the entire genre, I'm so much better at it it's kind of embarrassing(2). We have roughly the same intelligence, know the rules equally well and love to play it...but even though she grasps the concept of strategy, it's...somehow harder for her to actually see certain options. She often appears to be stuck whereas I see opportunities.
(note: I could bang on about skills and improvement all day, but I think this'll suffice).
(1): on hindsight, I was WAAAAY too young for this one
(2): I often even pretend to miss one or two victory cards, just to make it seem more close