I really enjoyed this piece! I can't speak about Japanese (or in general language that force you to learn new alphabets), but you can absolutely learn English with videogames! Maybe it's difficult figure it out for English people, but for European is just normal learn language through vg, tv series, movies, books.
My gamers generation, grew up in nineties, used to learn a lot through vg and above all rpg: most of them wasn't translated so you was forced to play with dictionary between your knee (you can hear a lot of story like this). Before Final Fantasy VIII all rpg, full of dialogues, weren't translated so you have any choice. Even now, 20 and more years later, I had to spend 120 hours on Persona 5 in English, because Italian wasn't available until Royal.
In a bigger picture, I learn't so much with subbed tv series.