> When I read ‘they’ I think plural people not singular like ‘he.’

I'm sure you're aware that it's usually obvious in context, like many ambiguous uses of language. For example,

> Every time the player has to restore a saved game, or pound [their] head on the desk in frustration

Changing "his" to "their" doesn't make the phrase any more difficult to read, imo. Maybe it's just something you'll pick up with practice.