Any version of Family Feud after the Dawson version. When the later versions started, there was no need to re-explain the rules.
Who stopped mentioning the goal score during the first question? I know Ray did it, but I remember Karn doing it when the goal score was re-established, and then never seeing O'Hurley explain it.
I think O'Hurley and Harvey mention it going out to the first commercial.
What I meant originally, though, was...aside from the point goal, every version besides Dawson's did not (need to) explain how the game in general works. Think the first weeks or so of Dawson was the only time I heard the game explained in detail during the first Face-Off. ("XX people said it, that goes into our bank, now here's how you build the bank...") Though just saying "try to find the most popular answer" is the show in a nutshell.
Aside from obvious cues during the game, Combs and the current version did not start with the "101" explanation that the show did when it debuted.
This may be cheating, but...the Money Cards in Eubanks/Rafferty Card Sharks when the car game was being played.
Everyone knows how to play Password, even Allen said that much on the first PW+ episode.
The stand-alone Hollywood Squares averted this pretty much, as everyone did the "three stars in a row" spiel for as long as the show was on. Except I think there was a time or two Peter just said "Our contestants know the rules" or words to that effect...maybe I'm thinking of the NBC finale? And later on, Bergeron simplified the rules spiel. Actually, only MG/HS seemed to assume we knew everything, since Bauman only explained the scoring and that whoever's ahead wins the game.
Wheel is like that too...of course it's been around for 40+ years so I'd hope we know how to play it. But for most of its existence, the only rules explanation was how the wheel worked (what the top value was and don't hit Bankrupt, essentially) with little said on screen about the puzzles. Then less so when they went to all-cash.