Not necessarily.
To say “I am a Gamer” implies that I play games as my main hobby and it is my main source of fun.
Mobile games are filled with ads, microtransactions, and are (mostly) not professionally made.
If someone were to say “I play candy crush so I’m a gamer” he is insulting all gamers by associating himself (who plays the lowest form of what can be considered video game) with people that actually appreciate the value of a $60 game and are willing to pay it for actual fun. Not ads, microtransactions, made to addict, and all around unprofessional games