With the growing popularity of computer games and the rapid development of this industry, it seems critical to have an up-to-date classification of computer-game types that won't grow old as quickly as the genre-typed did. The study investigates the relationship between computer-game-type preference and personality traits in the context of O. A. Popov's classification of computer games. Split into two dimensions - having a playable character and an ability to make moral choices - young adults show numerous significant differences in levels of computer-game addiction, personality traits, self-regulation, and moralities. People preferring-existing-of-playable-character-or-characters-games appear to be more introverted, having problems with self-regulation, and having weaker moral foundations while being more open to new experiences. Preferring-to-have-moral-choices and haven't-decided-on-moral-choices show the same observation with the addition of less agreeableness and exception of moral foundations. Moreover, haven't-decided-on-moral-choices appear to be more greed-avoiding than preferring-not-to-have-moral-choices.