Yep, these Briggs with the Walbro LMS carby use a 'dry primer'.
This primer pumps air into the float bowl vent, via a gallery in the air cleaner base, a hole in the gasket, and another gallery in the carby flange. The air pressure forces fuel through the main jet, and thence into the venturi.
So for it to work properly, there has to be a very good seal between the carby flange and air cleaner base, and around the hole in the gasket between the two. This is the small hole just below the left hand bolt hole in the carby flange.
That gasket shown in the pic won't be up to the job any more. While gasket paper is easy enough to get from auto parts shops, as a one-off it would be cheaper to just buy a genuine gasket, as it's a very fiddly one to cut.
These primers can also leak air if the sealing surface of the air cleaner base isn't flat any more, so be careful the bolts are not over-tightened.
