Tim Harrod sends this one in. “So… now he’s sitting on a giraffe. And kings rarely do that, and that’s the joke? The whole joke? No dialogue to nudge us in the right direction?”
The previous day doesn’t seem helpful here.
Giraffes aren’t ridable due to both structure (sloped back) and attitude. They are kissable, though.
Comics I Don't Understand 
I think that the joke is how hard it was for the king to mount the giraffe and how pointless it proved to be. Neither the king nor the giraffe seem happy about the arrangement.
The giraffe and the spectators are not impressed, but those eyes reveal that the King is inordinantly pleased with himself. The whole point of the strip is based on an ancient running gag in “The Wizard of Id”: the King is very short, and he was always looking for ways to compensate for his stature (he once even had himself put on the rack for a “stretch”). He may still be short in the third panel, but he now has the tallest “steed” in the whole Kingdom of Id.
P.S. Unfortunately, the GoComics archive doesn’t begin until 2002, so it is missing the first 38 years of Id history. Those early strips are therefore very hard to find.
P.P.S. Just by coincidence, today’s “Wizard of Id Classics” has a height joke from 1974:
“Giraffes are kissable” is the factoid I needed on a very gray day. 😁
“Giraffes are kissable” is the factoid I needed on a very gray day.
So it’s Grade A information?