Yes, the engine you swapped in (the OBD1 engine) DOES have a crank position sensor. The sensor you're thinking about is the crank fluctuation sensor most likely, which is on OBD2 engines only, and usually only on USDM engines. This is NOT the same as the crank position sensor, though it is on the crank. The crank position sensor is still in the distributor.

If you want to use the OBD2 ECU, there are ways to bypass the crank fluctuation sensor, which I think just involves tying both ECU inputs to the crank position sensor in the distributor. You'll have to look that up to be sure, I've never done that before and I don't want to tell you the wrong thing.