And if so, does that mean your dad sleeping with your mom is also NTR? Did your dad NTR you so you could be born? If not, at what point after conception does it start being NTR?
If the core of NTR is someone who "belongs" to someone (whether that be girlfriend, sibling, parent, childhood friend, or even just unrequited crush) being "taken" by someone else, then arguably your dad boning your mom isn't NTR because his claim on her predates yours (and your literal existence). You can NTR him, but he's not NTRing you (unless, theoretically speaking, something happens in the story where he "forfeits" his claim and your mother promises herself to you, but he still comes back to "steal her back").
But that would be one of the few exceptions, because almost every other possible combination (even siblings) involves the protagonist having "first claim" on the chosen love interest. Scenarios where the other guy "got their first" (even before the protagonist knew they were interested) like a teacher having a fiance or an aunt being married, etc, might not be NTR theoretically, but can still generate NTR-esque feelings in the protagonist (which usually becomes the fuel for netori stories).
People can quibble over the validity of whether or not someone has a "claim" on the person in the first place (ie, does your childhood friend or childhood crush "belong" to you if you never actually entered a romantic relationship with them?), but generally speaking stories tend to assume that the protagonist's perspective is correct - so if they feel as if their mother/sister/childhood friend, etc. "belongs" to them, then they do. At least for purposes of the main character feeling cucked.
What makes it more complicated is that, when you're talking about a game where the player gets to make choices, the "protagonist" isn't necessarily the main character as much as it is the player themselves. So even if you write the story to make the main character completely fine with the idea of a dozen other guys gangbanging his mom, that doesn't mean the
player is going to be okay with it.
Which is what I think is at the root of most NTR hate on the site - if a game is going to force the player to pimp out their love interest or get cucked without giving the player any ability to say no or
stop it, then there will almost certainly be a significant backlash. It doesn't really matter if the main character gives permission for swinging or sharing or prostitution or whatever if the player doesn't.
The player isn't getting cucked any more than the characters in the game are.
There's an argument to be made that a game that expects the player to identify with the main character (mainly by showing their pov, but also by asking the player to make choices for them), and then forces the player to watch other characters fuck without the player giving approval
is triggering the same sort of feelings as NTR (at least for some players).
That's why, essentially, when most people on this site say "I hate NTR!", what they're really saying is "I hate not being given a choice!" Games that allow the player to completely avoid those sorts of scenes (
avoid, not just "skip") tend to do much better than ones that basically go "The character is okay with it, so shut up."
That being said, the point where the player got to make that choice in THIS game was when they decided to play "Mom Swap: The Game" in the first place. So it's hard to feel bad for someone who gets halfway in and is annoying to see two dudes fucking each other's moms. It's sort of the entire point.
But games where the NTR-ish content isn't the main focus, and is "hidden" somewhere towards the middle of the game is far more likely to stir up an angry reaction from people who feel like they've been betrayed, or had player agency taken away from them.
To bring it back to the first part of this post, there's a difference between knowing that your dad is fucking your mom, and being forced to
watch your dad fucking your mom.