I think its just elitist to call playing on mobile phones as "not gaming". Sure, most mobile games are very casual, but there are some people who spend a lot of time on them and get reall really good, just like more, "advanced" gamers. That being said of course, there are people I've come across who describe themeselves as "hardcore gamers" and go around talking about how cool their "gaming" world is and they just play mobile games, and I find that really irritating.
But in the end, I think this topic will be a debate for just around 5-10 more years. More and more PS4, PS3, and PC games are getting their android/iOS versions too and I think playing those is just as acceptable as playing them on a console or PC. For example, Mortal Kombat X is out on Android for free, and has almost the same features as that on PC or console, so I thought it was a far better option than having to pay for it, plus it is handy too, you can play even on buses and the subway.