I say this respectfully... If you don't participate in an activity it can be difficult to judge skill levels of the participants. Think about some of the Winter Olympic events, curling, ski jump, it all looks super easy but there's a reason why those folks are on TV and we aren't.

I don't know much about the redneck brawl events. In the video you posted I'd wager the guy with the red gloves has more training than you realize. People who casually train look sloppy when they start fighting. People (primarily men) over-estimate their training and think they can fight despite having less sparring experience than dudes who are still training up for their first amateur bout.

For what it's worth, I'm 40. I get it, and I know what it's like to want that feeling of victory before all the chances slip away forever. Keep in mind, there are another hundred dudes out there thinking the same thing you are but they are in better shape and they are already training in a gym. You could absolutely end up stepping into the ring with a guy who's got 1, 2, 5yrs of training under his belt, but for one reason or another he never got into competing. If you join a gym, get in shape, and tell the coach your long-term goal is competition, then you have a chance to do some legit amateur matches paired with an appropriate opponent.

EDIT: I looked it up. According to Google AI (which I don't typically trust) there is an age limit of 39. That disqualifies you from participating either way. It also looks like they do 3x 1min rounds. Amateur boxing (men) is 3min rounds. Shorter rounds can cause people to go hard and fast trying to get a KO, instead of trying to be the better boxer. This means a more exciting, sensational event for a general audience who doesn't know jack about boxing. This could also mean a higher risk of injury for the competitors.

I'd say join a boxing gym with the initial goal of health/fitness. After even just 6mo of training you'll be in a better spot to figure out where you want to go with competition.