A few observations about my group's style (hmmm, it could use a fancy name... "The Style"... no... "De Stijl"... too Dutch... "Duh Stijl"... closer... "Derp Stijl"... that's it!)
It's system-independent. We tend to play different games the same way in the end; system doesn't matter nearly as much as our personalities & collective sense of humor. Over the past decade our extended group has managed to play D&D 3e, M&M, Dragonstar, D&D 4e, Savage Worlds, AD&D, Fate, and D&D 5e in a similar fashion.
It's very character-oriented. In the sense the goal is to create the most amusing, if not absurd, fictional characters & send them on amusing, if not absurd adventures.
Regardless of system or genre(s), we flirt shameless with parody & satire. Probably because they look so good after a few drinks.
Despite being silly a lot of the time, the (usually homebrewed) settings tend to be detailed. Because some of us are inveterate world-builders.
Sometimes, the silliness pivots to serious, philosophical, even poignant (when someone other than me is DM'ing). Those moments are kinda magical.
If our campaigns where Infocom text adventures, they would have 2 modes: VERBOSE and EVEN MORE VERBOSE.