Date, flight #, departure airport, arrival airport? Details matter.

First, send a note to UA and to DOT (online form) in which you provide the exact facts which you personally witnessed and a description and seat for the passengers who said that the guy had been drinking in the UC and appeared confused.

Second, forget about "compensation" from the drunk. You won't even be able to get his name without first obtaining police reports and UA records and depending on the flight departure/arrival information that may not be as easy as you might think.

Third, if you want to approach UA and advise that you are going to contact an attorney unless some sum you consider to be reasonable is paid in cash within X days, go ahead. Otherwise, hire an attorney. Some might do this as a cut of the loot. But, either way, it costs you $. The key to an attorney is that it needs to be someone who deals in aviation cases. You may think that this case is worth $10K, but in reality it would likely only generate $1K even after a trial. That is where an attorney helps.

Fourth, part of any deal has to be that UA provides the name and contact info for the passenger. That may be part of a settlement with UA. Maybe the guy has not a penny to his name. Maybe he is the EVP of a large company which will pay up quickly. You won't know that until you check out the facts.

Collecting from both UA and the drunk will be separate, but the amount paid one will be taken into account by the other.

Or forget it and move on.