I am wondering if the male coworker has his own medical issue that is causing this frustration. Perhaps he has IBD? Older males also sometimes have urinary continence issues, and it's kind of uncomfortable to discuss them with coworkers. Pissing one's pants due to not getting to an available bathroom can be upsetting. If not, his behavior was boorish.
I have always worked for smaller firms so any issues as between coworkers usually gets discussed openly. Last week our office manager was very upset that trash wasn't being taken out of the office kitchen and circulated an email to the entire staff (which is 12) on this issue and her concern was that rodents will soon be attracted to the kitchen. I later teasingly told her that if any rodents are around I will get a rat zapper on Amazon which will eliminate them.
My own opinion on an issue like this is direct communication with the coworker should be utilized. I would only go to HR if direct communication doesn't resolve the issue. Although I understand the role HR plays on issues like this, my sense is that people who are quick to go to HR on an issue like this might start to be seen as not being "team players" with their coworkers. I go out of my way in my small firm environment to try to adapt to the needs of my coworkers and to be seen as a team player.
It sounds like the company's bathroom setup is female friendly, although that's not always the case with public restrooms. I used to train to Grand Central Station in New York City regularly, and always remembered seeing a very long line extending out of the women's bathroom but none extending out of men's bathroom. Where there are urinals men are easily in and out, so my conclusion without ever having been inside the GCS women's bathroom is that there was likely an equal number of toilet seats but higher demand obviously as women need to sit down. I could never understand why they didn't equip the women's restrooms with more seats. Always felt sorry for the women caught in those lines after stepping off a train, and used to wonder if any of them had IBD.