The sprockets need to stay in alignment and the chain needs a little slack. Is the chain stretched or more likely, are the axle bushings worn out?

It may be that the chain has worn enough that you have too much slack.
I'm absolutely unfamiliar with your machine, but is it possible to loosen the engine mount (or something similar)and slide it some to take up the tension?

If you need to replace the chain, check for a master link. IF it doesn't have one, you could possibly use a chain tool available at a bike shop for about $6.
Depending on the chain pitch etc., you could probably get new chain at a "power transmission" type store.

I have no play in the axel bushings. Is there a better way
to tell if the bushings are worn out?

The chain could be stretched I suppose..If I have to tear it down to replace the chain, it seems like I should also
order most of the other pieces (drive shaft bearings and
drive gear). It looks a little funny up there. The shaft
looks to be tilted ?? but as I noted before there doesn't
appear to be any adjustment. I loosened the outer bearing
screws but it there was no adjustment to be made there.