Why isn't he wearing a loincloth?

Because it's Yukari's fantasy, and she imagines him dressed properly for the occasion.

If it were Kourin's dream you could expect a lot of mannosukeesm and fundoshis

If his dream was even this to begin with.

It's not.

I guess I'll call Rinnosuke 'Jijii' then...

This pool description is wrong. There's a big difference between being a troll and being an ass, though they're not mutually exclusive.