I have an old Texas Football magazine, from 1969, which has an article about old trick plays, mostly from the 1920's, written by sportswriter and cartoonist Bill McClanahan, and he also has several carttons illustrating the plays. One he describes was much like the point of the video here. An offensive team was penalized 15 yards for holding. The team lines up for the next play, the TB says, "Wait a minute, Mr. Referee; 15 yards for holding? Wie, holding is just 5 yards! Give me the ball!" So the center tosses him the ball, he steps off 10 yards as the defense just watches, then he takes off. There was no rule that the center had to snap the ball to a back then.
If you remember the "fumblerooskie" play pulled by Nebraska in the 1984 Orange Bowl and by Oklahoma in the 1988 Orange Bowl, that differs only slightly from another play McClanahan talks about-- the "hidden ball play." Again, with no rule that the center had to snap the ball between his legs to a back, he would hand the ball to a guard beside him, who would squat down on it, while the rest of the team took off in one direction. Except for the opposite side end (or tackle), who would come around and take the ball from the guard and run around the vacated end. The fumblerooskie play differs only in that the center did have to put the ball between his legs, so he put it on the ground and to one side, with the QB's help, instead of handing it to a guard. One reason the center has to snap the ball was to cancel that kind of a trick play, so the fumblerooskie was the updated method to keep it legal. Later, of course, that play became illegal, too-- an offense is not allowed to deliberately put the ball on the ground intending to deceive.
One more I'll talk about, which if not illegal now is almost impossible-- though perhaps not at some high school competition-- was the "dead end" play. During a play with the action on the opposite side of the field, an end would go down and stay down, making sure he was behind the new scrimmage, and maybe having to 'sneak up' to be within a yard of the line. He was hoping the defense would not even notice him until the play began, which obviously was a pass play to him, very wide open. That sometimes worked in the 20's and later, because the fields many teams played on were not nearly as well kept as most have been since WWII. The grass was often tall enough to conceal a player from the other side of the field; and hash marks were closer to the side, too, so he was further away from the rest of the center of interest.