Are runs allowed with emulators? I know that some older games for NES/SNES/GB allow them but, but there's no listed "Game Rules" for this game at all so... yeah.

According the rules, you must collect all "9" hats, but given that with the The Sunset Station update there's now an additional 15 hats, should the category not be renamed to something like "9" hat with all the runs as present moved over there, and a new "all hats" category created to include the additional 15?