Earlier quoted context omitted.
I get your point, but I think it's more accurately framed like so: "Over three billion people are now drinkers" "If you count having a glass of wine once a week then sure" The perceived snobbery is less about whether these people are playing games and more about whether they can be accurately described as "gamers", a term which has meaning beyond simply "players of any game(s)" due to its many (largely negative) conn…
I'm confused why there's some implication of diminished frequency with "casual" gamers. On the subway, it's not uncommon to see people playing games like candy crush on their commute to and from work. The average subway commute is an hour long each way. Playing two hours a day is a decent chunk of time. Engaging in any other hobby for even 30 minutes a day would put you squarely in at least the "enthusiast" category…
It may have to do with the difference in "I will play this game instead of staring into the void" vs "I will buy that game and set aside time to play it". Would people on the subway play candy crush if they didn't have to commute? There's a fine line, I believe.
And then there's another fine line with regards to what counts as "video game". Is computer chess a video game because it's played on a computer, or is it simply chess? How many people would say "I'm going to play on the computer" vs "I'm going to play some chess" when they're going to play chess on their computer? "Video games" aren't the same as "mobile games" in my opinion, though there are video games on mobile devices, but e.g. Solitaire isn't a video game.
And last but not least: I'm pretty sure most people who play Minesweeper on their commute but aren't otherwise into computer games would self-identify as "gamers".