“his holidays” sounds like they are his days off, whereas “the holidays” or “holidays” might mean more something of a community-level holiday: for example, Christmas, New Year, national holidays, etc. What can you say when you’ve done something stupid or clever? In American English, though, most people don’t say “his holidays” – rather, they would just say “desk days off” or “weekends” depending on their intent.

I believe in Australia, “holidays” are used to refer to days where you don’t need to go to work, so “his holidays” mean that, while “holidays” would be more general and apply to everyone other than him, and mean days like Christmas and New Year.