Define game :

1) A form of competitive activity or sport played according to rules.

2) an activity that one engages in for amusement.

Depends on what you expect in dota. Some may play for fun , some may play for pride , some do play very seriously in order to go into e-sports.

There is no right or wrong here but if playing a game makes u depress / anger / emo then i think it starts to defeat the purpose of a "game".

Or maybe Dota 2 in not a game.