I'm not at all clear on how many tables there are; is the 'applying the Filter formula in an Excel table' the same table as BkgTbl?
Putting the Filter function within any table will probably have Excel complaining.
Are you trying this:
=FILTER(FILTER(BkgTbl[[#All],[Group]:[Rtn Depart Time]],({1,0,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1})),BkgTbl[[#All],[BkgRegT]]="Yes","")
if so, you'll get the same result with the shorter:
=FILTER(FILTER(BkgTbl[[Group]:[Rtn Depart Time]],({1,0,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1})),BkgTbl[BkgRegT]="Yes","")