It looks as if it may have a valve rotator, which would be unusual for a side valve engine. I can only recall three types of retainer Briggs used on the old side valve engines: the keyhole type, which we are all used to on the small engines, and can be seen on your inlet valve; a lateral pin through a hole in the valve stem; and an automotive-type split cotter. In your picture it looks like the valve has the groove for a split cotter, but I don't see the cotter.
The easy way to clear up all these mysteries is if you just post the Model, Type, and Code and we'll have a look at the Illustated Parts List. We'll also be able to look it up in the Briggs repair manual.
