Your engine was made on 30 September 1975.
Here is its illustrated parts list:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6jmvGVJ1DajI.pdf

Here is its operator's manual:
http://bsintek.basco.com/BriggsDocumentDisplay/lrvvA-wU7eL7hAxB91ObQ.pdf

The important differences between the 80102 and 80202 relate to the carburetor and choke, and the engine kill switch. The 80102 is almost the same as the smaller 60102 which I think was used on the smallest of the SB45 mowers. I find that choke infuriating, I always have to start them chainsaw-style (it rich loads and stalls before I can push in the choke, after a cold start, so I have to start it twice). However the engine should be just as reliable and durable as other old Briggs engines.

I won't confirm that you don't need any parts: you are going to have to buy a new plastic thrust washer for your clutch, and perhaps another part too, to get it working properly. However that is Deejay's line of country.