I wonder what this was about? There's no way we can ever know for sure what the thinking about this was. The aptly named Terrible Trio were such bad villains that maybe they though having Dr. Doom on the cover, even as a gag,l would sell a few copies.
Hoy
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I'd guess Kirby assumed there'd be text about how he gave them their powers, or was told to put him there, and Lee put that information into the top caption instead and was just feeling silly when he wrote the lower caption.
Alternatively, it could be the box was a late addition, added because Lee thought the corner too bare.
It's also possible the cover was drawn before the story. Perhaps Lee hadn't decided he wouldn't appear in the story when it was done. He actually is seen in the issue, in the flashback.
The most plausible explanation is that the cover was drawn first and Lee intended for Doom to play a role in their return, as he had in their appearance against the FF. But then he didn't bring Doom into it directly and had to write something for the cover. He decided not to overplay Doom's role in the story and went a bit overboard.
Or, alternatively, he planned to say "See how the Trio performs now that they are free of the direction of Doom!" or something like that. And when he saw the cover, he was just in a silly mood.
Because in fact it's a lie! Doom DOES appear in the issue! It's all in a flashback so he's not in the "story" directly, but he's on several pages. albeit not taking part in any action. So it's an even stranger thing than it seems.
-- MSA
I don't think it was a cynical move. Possibly Stan wanted to remind readers who the Terrible Trio were. I bought this when it was new. There was a lot of playful kidding going on which made the fans feel like insiders. It fit the Marvel mood then.
Probably a contractual obligation thing, where Marvel was obligated to run X number of covers featuring Doc Doom's mugshot, otherwise the Latverian Ministry of Finance would be due a hefty payout. Being notoriously cheap, Marvel opted to use Doom as often as possible to fulfill the terms of the deal.
That is undoubtedly the correct explanation.
The issue came out the same month as Amazing Spider-Man #14, which has an inset box with the Hulk on the cover, and Daredevil #2, which has a Thing head and jokey caption on the upper left. The next month Amazing Spider-Man #15 had a Chameleon inset circle and Strange Tales #123 had inset boxes with the Thing and Thor (with jokey text in the Thing's).
A Silver Age "Assistant Editors Month"?
Stan seems a bit confused. That's not Doom's face.