It was their second performance on the show, probably from mid August '64:
Mack says "it's hard to believe summer's practically over but fortunately talent knows no season" ...
then says "three weeks ago some young men from Maplewood, Metuchen and Montclair NJ opened our show with an instrumental number but due to technical difficulties on a good portion of the network most of the people couldn't see their full musical turn, so we thought it only fair we bring them back and give them another chance so here they are the Chessmen"
If you view a bunch of these shows I guess you could cross check it with Mack saying he'll "spin the wheel of fortune for the 1,504th time"
Also you could check the TV Guide for the next act "Ike Jones".
'64 does seem kinda early, despite the band's look & the Rickenbacker, their material is very Stones-like & the singer has a definite Jagger influence. The Stones did a brief US tour in June '64 and appeared on Dean Martin's TV show in Hollywood, but hadn't really hit in the US yet. 'Hoochie Coochie Man' wasn't too well known either, until Manfred Mann put it on their LP in Sept. 64. Not impossible though.
Great clip!