The playing thing is ok. Just put him in bed with some books and toys, tell him he can read or play but he has to stay in bed cos it’s night time.
Meg is often to be heard playing happily away with her toys at 3am. She goes back to sleep in her own time.
DO NOT play with him or entertain him in any way, cos he’ll think nini time is actually daddy playtime, which it’s not.
However I would like to add that with us, waking was almost always food related. She’d sleep through normally but go through a period of waking up and crying a lot. We figured out that she was just hungry. In our experience her calorie requirements vary dramatically depending on if she’s having a growth spurt or not. So she goes from eating hardly anything to being a complete ravenous monster waking up starving in the middle of the night. We found Ellas Kitchen fruit/veg pouches were good for this.
Grown ups also wake up hungry of course, but remember they can go downstairs and eat last night’s cheesecake if they want.