The difference between anime and LA is greater than the difference between a blue tie and a red tie. Anyway, many restaurants operate a dress code. Plenty of places only allow formalwear and plenty of places won't let you in if you're too dressed up. The restaurant owner or manager gets to decide what the dress code is, and from that, who gets in. So long as they tell you this before you book a table, that's their right.

It's the same thing with games.