The engine will work OK with the smaller muffler, but you may be losing some power that way. We used to run much worse mufflers than that on engines years ago. The engines weren't the worse for it, even though they lost some power doing it. The smaller muffler may be a blessing of sorts in disguise too. ASP tends to put carburetors on the engines that have too large of a intake venturi bore on them. That results in poor fuel draw and more dependence on muffler pressure to compensate for the lack of fuel draw ability. Thus the smaller muffler would increase the muffler pressure a little more and it may help. Heck the original owner may have had that problem too and went with the smaller muffler.

Since you test ran the engine already and it worked fine for you, then go ahead and use it like that. You can likely find a new 1.20 muffler someplace, but if the smaller muffler works, I would not put much effort into it.