This quote from the Vulture article seems to explain Buzzr's rationale pretty well:
But reviving MGHSH also lets Buzzr give its game show diehards more episodes of the very popular Match Game format (the ‘70s version runs multiple times each day, while ABC is now airing a revival in primetime) as well as some form of Hollywood Squares, reruns of which haven’t been seen regularly in years. While Deetjen would likely be very open to the idea of airing the original Peter Marshall-hosted Squares, Buzzr parent company Fremantle doesn’t own the rights to it (unlike most of the other games on the channel). “This is a way to slide in Hollywood Squares to our lineup,” he says. “If you were to do a Mt. Rushmore of game shows, it and Match Game would both be on it.”
Quite possible, I mean they had to talk to MGM, didn't they?
Anyway...I will say that with all the complaints about elements of the show...I'm glad to see it again. Nostalgia and all that. It'll be surreal to have pristine copies on TV now, just like it is with Classic Concentration.
On the topic, and in line with what I've asked around about...there's two related items I wonder whether or not they can be (re-)found. One is a picture of the floor mural at the original location of the NBC Experience in NYC. As this featured shots of their shows over the years, and included Squares...but not the Marshall version. No, they not only chose a scene from the MG/HS version, but the PILOT set (host/contestant area is all grey, not red, yellow, and blue). That one's on par with the 80s magazines that did reports on video games and used CRAZY OTTO screenshots to represent Pac-Man.
Second thing is an interview I recall being posted online with Gene Rayburn. Notable because they did touch upon MG/HS, and while he was savage against BTB '85, Gene was much milder talking about the earlier show...even saying his "hated co-host" Bauman was a nice guy but didn't have hosting chops.