1) It's hot, so you want clothes that work well for that, similar to biking. Loose pants and a cotton T-shirt may work for regular yoga, but you'll die in the heat and humidity with Hot Yoga.
2) Running shorts work really well as they're short and lightweight. However depending on the pair they bunch up when you move from one position to another, to a point where I'm physically restricted and have to un-bunch the leg so I can move freely. Some shorts that happens, others it doesn't.
I'm just going with what works, people do different things. But if you do hot yoga long enough you realize the people who do it a lot wear next to nothing. Guys that aren't fat like me are topless, girls in sports bras. Women I've noticed do the short-shorts often lately that aren't loose like traditional running shorts.