Eh. No, that's not quite how that works. If you look at north american elementary school level reading, you may notice that books are often categorized by levels. Some of this has to do with complexity of sentence construction, some has to do with vocabulary, and some has to do with subject matter. The gist of the educational philosophy around reading is that one doesn't get better at reading by plowing through reading material at high volumes, but instead one needs to gradually level up by going through materials of appropriate complexity. One specific problem that teachers look for - especially in kids that advance quickly - is "skimming without understanding", for example (i.e. reading words/sentences phonetically, but without understanding their meaning/context).
Game text is usually not structured with any didactic value in mind (other than maybe appropriate usage of furigana in Japanese in consideration of target audiences). A lot of game categories don't even require any reading beyond recognizing words (which is somewhere between kinder and 1st grade level reading skill)
Also, even in games where text actually matters, you're typically spending a large amount of time doing other things (killing monster or whatever). In addition, the notion of games-as-reading-material ignores a fairly common phenomenon: a lot of people simply spam `A` to skip over dialogues - and even get stuck on one-off gimmicks that rely on reading the text carefully for instructions or clues.
To be clear though, practicing pre-acquired reading skills can help in the sense that repetition legitimizes, but IMHO that's a bit different than improving beyond a current level, and not necessarily all that different from what you get from reading cereal box/shampoo labels or reading comic books.