It doesn't really work for anybody who's not a 'hardcore gamer,' but many fighting games (CvS2, MvC2, SF3:TS, KOF2KX, etc.) and shooting games (Dodonpachi, Ikaruga, Psyvariar, etc.) would fit this bill.

However, that's only if you're 'hardcore,' because fans of these genres don't consider the game to be over when you've seen the credits roll by. Combo extension and competitive skill, or score-improving, are ongoing goals that span multiple sessions; 'beating the game' is barely even a milestone. I guess it's not really a 'casual gamer' aesthetic, but if you want a game that will occupy you for months and months, that's what you're looking at.

MvC2 is probably still the most competitive 2D fighter in the US; it's been out for 6 years, maybe? People still play Super Turbo in arcades near me. That's replay value for you.