Russell Mulcahy (the director of the video clip for 'Allentown') and Billy Joel both discuss that video clip in the oral history I Want My MTV by Tannenbaum and Marks.

According to Mulcahy:

Billy Joel’s “Allentown” has homoerotic imagery...

Well, if you wanted a TLDR for this post, there it is! Mulcahy explains further:

...there were shirtless construction workers. And there is bare assery. We had to pay the boys $500 each to show their asses. I think it was the first time bare ass had been shown in a video. Don’t forget, that was 1982. There’s been quite a cultural change since then. That was many years before I did the pilot for Queer as Folk, where the first day of the shoot I had a guy’s tongue up another guy’s ass.

According to Joel:

In The Hangover Part II they did a very profane and hilarious spoof of “Allentown.” There was renewed interest in the video on YouTube, so I watched it the other day for the first time in a while. Now, Russell was a brilliant director. But I didn’t realize until I watched it again how gay that video was. It’s really gay! There’s a shower scene with all these good-looking, muscular young steel workers who are completely bare assed. And then they’re all oiled up and twisting valves and knobs. I’d missed this completely when I was doing the video. I just thought it was like The Deer Hunter. You know, guys go off to war, they come back, they’re all messed up, and there’re steelworkers who don’t have jobs—okay, I get that. But did they have to be taking a shower with their bare asses hanging out? Maybe there’s something artsy-fartsy about that, I don’t know.

For context, 'Allentown' was released as a single in 1982, in the very infancy of MTV, at a point when nobody really knew what would work on MTV, and when video directors often treated the musicians as recalcitrant interlopers on videos for their own songs. Russell Mulcahy (a gay Australian man who later went on to direct Highlander and its sequel) was one of the biggest names in music videos at this point, having got his start directing a video for Australian punk band The Saints' I'm Stranded, and then going on to direct 'Video Killed The Radio Star' by the Buggles (famously the first song ever played on MTV). Other directors in 'I Want My MTV' pay tribute to Mulcahy:

BRIAN GRANT [director of 'Physical' by Olivia Newton John): Russell was probably the most successful director of that era. Everyone wanted him to direct their videos.

MARTY CALLNER, director: I was in bed one day, watching a pay cable station called the Z Channel, and a music video came on: “Bette Davis Eyes,” directed by Russell Mulcahy. It broke every rule of what is and isn’t allowed on television. It was the most creative thing I’d ever seen on TV.

Billy Joel, as an established star from before the MTV era, knew that MTV was the new big thing and that he had to start making proper videos, and like many of the stars of the era, he wasn't quite sure how it all worked:

Russell directed my first real video, “Pressure.” I put myself completely in his hands. I said, “What do you want me to do?” He said, “You’re gonna sink into a pool of foam and disappear.” “Okay.” “And then you’re gonna be in a chair raging at the sky.” “Okay.” “And then you’re gonna walk down this bridge.” “Okay.” It was his movie, his vision. I didn’t know what any of it meant.

So yes, Mulcahy (who also directed the video for Elton John's 'I'm Still Standing', which he himself calls 'super, super, super gay' in I Want My MTV) absolutely knew what he was doing with 'Allentown', even if Joel was a bit clueless about it all.