"Henry, say goodbye to the one person in the world
Who could have stood between us and everything in the world worth stealing."
"THE FINE ART OF CRIME"
I saw no reason to doubt Mr. Moreaux's claim. So if he was fixated only on Wonder Woman, then he knew Superman was no threat to their plans whatsoever. And so I view that as a confirmation that the Man of Steel had passed away back in the early 1960s.
Batman was probably still in the "biz", but as he wasn't super-human and because he was centered in Gotham City, then he was no threat to Moreaux's current plans in Washington, DC., or anywhere else in the world for that matter. This would be the excuse for any other super hero, supernatural being, or general do-gooder - even Mr. Terrific and Captain Nice! - to be unavailable to stop Moreaux's plans: location, location, location.
And Barry Allen didn't gain his powers as the Flash until 1990, so Moreaux didn't even know of him as a threat yet.
Of course, there was always the Hulk, but he wouldn't purposefully be seeking out the mastermind behind the art world thefts. And being mostly a raging brute on a destructive rampage, the odds were pretty high against him ever crossing paths with Moreaux and Roberts.
As long as Moreaux didn't fall into any pattern to his crimes, as he did during this episode (although that was just to lure Wonder Woman into a trap), then not even the super sleuths of the world who were working at that time could have anticipated his next move.
About the only one I could still see as being a viable threat would have been the Gallifreyan Time Lord known as the Doctor. But even he would have stumbled into an active crime scene rather than be actively seeking out Moreaux.
On a side note, since Wonder Woman was around during the 1950s (being practically immortal), it is left to our imaginations to picture her working with Superman - as played by George Reeves.