I don’t know that answer about the riser/tread question without looking it up in IRC code. However, when the riser and tread are connected together in a secure manner as illustrated in your picture, you obviously have much greater load capacity. Nothing wrong with that tread and stringer design in my opinion. Good thing to look up in the code book if so inclined. When dealing with old construction, one method I use is to walk up/down the stairs, do the “jump test” - does it pass?
Lots of old homes, especially cellar stairs, were built with 2 x treads, no risers, and two stringers built with 2 x 10’s. I’ll call that out with the caveat that building practices have changed since the time the stairs were built. Issues: safety for the buyer, liability and credability for me if I don’t mention it. It’s your call and opinion on how you address old construction practices.