I haven't seen this, but I from reading the script as you posted it, I think I can help you.
How the hell did you end up in Processing?
Here, "Processing" is the name of some sort of department. I'm thinking of it like a Triage department in a hospital emergency room. To understand the grammar, it might help to think of "Data Processing" (except that here, it sounds like they're not processing data...).
What was it? Poker night? Bachelor party?
This means, did you get here as a result of a poker game, or a bachelor party? Because at a poker game, you might run out of money, and start betting something else, such as, "the person who loses this round has to go to Processing tomorrow." At least, that's my guess.
At a bachelor party, you might get drunk and wander around doing crazy things, and end up in a strange place like this.
No, sir. I'm from Kentucky.
Farrell is saying that his primary identification is as a person from Kentucky, and he feels that the Kentucky culture is strong enough that he considers it a separate culture (separate from the rest of the U.S.), as opposed to a sub-culture.
I liked that joke. I hope I didn't destroy it for you by being too pedantic.
"Late game" is part of a suite of concepts that are primarily used in two different kinds of games; multiplayer games with in-match progression (genres like MOBA, RTS, TBS, Grand Strategy), and games where the player progresses in power rather than through a linear story (genres such as MMORPG, ARPG, Lootershooters and many flavors of Roguelike). Games like these tend to have three phases; early, mid and late game. These phases are organic and defined by player consent, change on a per title basis, and are not formalized by the game itself. Games like Mario, DOOM and CS:GO don't have these phases. SWGoH seems to fall into the second category, so we'll focus there.
In this context, late game is when the player has stopped getting anything new, and is instead trying to get better versions of the things they already have. This phase never ends. The player continues to play and accrue power until they decide to stop.
"The next level," as a noun phrase, is a pretty common idiom in US English and is by no means exclusive to games. It is often used in advertising. It usually means a significant, easily noticeable improvement. A new fertilizer may bring a farmer's yield to "the next level." This is the context at work here. "Next level" can also be an adjective phrase. "Next level performance" is especially popular in the automotive advertising industry. "Next level thinking" is meaningless jargon in leadership consulting, but may refer to revolutionary strategies or concepts in other contexts.
Best Answer
There are a few [activity] night phrases that are commonly used to mean "a evening spent having fun doing [activity], usually with friends or family." The important implications are that the activity is fun and social.
Game night is an evening playing games, typically indoor games like board games, card games or charades. Usually it's assumed that one person is hosting several friends at their home (or that a family is playing together in their shared home). Sometimes the name of the game is used: poker night or D&D night for example. Under quarantine, game night has moved from being in-person to on-line in many cases, and that's what your referenced article is about.
Game night can also refer to watching an evening sporting event, either live or on television, again with the implication that it's a shared activity (either because you're watching in a group or because you're going to discuss the result with friends the next day). Fight night is similar and involves watching boxing or mixed martial arts. In Canada, the weekly hockey television broadcasts are called Hockey Night in Canada again referring to fun and trying to imply that watching hockey is a socially shared activity across the entire country.
Other constructions like this: movie night, date night, girls' night (meaning an evening of female friends having fun together). You can even use the name of a family meal (e.g., spaghetti night) with the implication that this meal is a particular favorite of most of the family.