First, lucky spoiled floof!
A lot of chins get a minimum of 15-20 mins a day. Depending on the time of day you are doing the playtime, that might have something to do with the sleeping. Chinchillas are more active at night, and it's taken a lot to explain that to my friend to pet sits when I have to be away. (Twice a year usually.)
Your chin may also be uncomfortable without something to hide under. Ours gets spurts of running about, chewing, playing, and then wanting to relax and hide somewhere for a bit again.
If you want, you can try a treat puzzle during playtime. (We usually just put a small piece of something in, not a lot.) Otherwise, if your chin is using the wheel and getting exercise, he's 100% fine.
Here are links to the chinchilla puzzles we use.