This marks the point where Snoopy begins to progress beyond just being a generic dog to being something strange and wonderful but, somehow, other. Like when Schroeder turned out to be a musical prodigy and Schulz could make jokes about an infant playing in a concert hall, now we have Snoopy with a TV antenna.
Those jokes are funny because the characters, up to that point, have been represented pretty realistically. Snoopy has always been a dog foremost and Schroeder was a baby before he became a musician. More locally, in the strips immediately preceding this one (and the last one, which also focused on Snoopy's intelligence) we had several strips which were about CB and the girls, depicting fairly normal happenings that could conceivably happen in real life.
As readers became used to the characters in their new roles, to continue to get laughs from them Schulz will have to vary his approach. In Schroeder's case he reins in the unreality a bit and has him play off other characters. In Snoopy's case he goes all-out, making him weirder and weirder. And weirder.
By the way, that third panel is just marvelous. Look at it, the whole joke is contained just in that one panel. It's an excellent sight gag. The panel could really stand on its own, Far Side-like; the other panels serve to accentuate it, but they aren't really needed. (Although Patty's looking back in the fourth panel, eyebrow raised, is pretty cool.)
