New guy here. I picked up this DT2 last week, 2000 miles ,18 years since it last ran. I’m cleaning it up and doing the standard checks before I try to start it. 
I pulled the chain to soak it and noticed the rear sprocket wobbles like a 3/16 inch.  Is this normal with that clutch thing in there?  

No clutch in there. But there are rubber dampers or cushions in there. So yes there is some free play side to side.

thanks…Clutch damper. I’m used to a sprocket being pretty much fixed 

They wear pretty bad in the sprocket carrier & hub where it moves but chain never seems to de-rail because of it. I've seen some extremely bad ones. No easy cure. I have a wheel from a TT250 to adapt to mine which has a bearing in the sprocket carrier which is similar in a way to what they ran in about "68--"70 on DT1's & should never have gone away from in my opinion.

The rear wheel that was on my RT2 had the sprocket bolted right to the aluminum hub. Is that a MX design?
Sneezles61

Sprocket cush drive is a good thing in theory & must take the shock out of the drive gear dogs & teeth. Seems more neccessary though in a motocross situation which is when they "don't have them from new". Well do in things like RT1MX etc but after that i guess everyone was becoming weight concious.

I read once that "shock" is not the main reason for the cush drive.  If I remember correctly, it has more to do with damping the harmonics of the chain drive which can apparently get annoying on some bikes at certain steady speeds on pavement? 

On dirt the harmonics are not as much a problem and of course a race bike should be as light as possible. 

I live & learn. That's good to know.

So when you goose it, it goes…
Makes sense MartT.
Forgiveness on the blacktop/hard surface sounds best.