On the top of my head it can be many things. It can be a financial problem (legal problem bank going to take the house). It can be drama in the house (with Max increasing authority in the house Alice start to notice and make a move and Ann who also depend on Max doesn't like that). It can be problem with Kira she may have ulterior motive for helping Max, she may social with a bad peoples so got threaten and kidnap if Max fail. Kate's mom may cause problem. The cop may start to looking for Eric so Max need to find a way to not be a suspect or he going to jail. et cetera et cetera.
Antagonist doesn't need to be a human it also can be concept that stands against the protagonist. Eric is a poorly design antagonist in term of both story and gameplay wise like a lot of members here already discussed.
I think Eric could've been excellent antagonist, he started well at the beginning by asserting dominance due to his age, money, and power advantage over Max. However, he was never allowed to really develop into a real threat. While I can't speak for DS, I strongly believe this is caused by player feedback of not liking another character getting it on with the female characters in the game. At that point, I felt that DS was forced to significantly tone down what Eric did. To me, this is a missed opportunity, but at the same time the reality of patreon-based game where DS basically just followed the poll result to make the game instead of making the game how it was meant to be made.
To be honest, none of your other alternatives for "game over" scenarios is any better than what Eric could've been. Not because they are bad ideas on paper, but they lack of the personal feeling. The reason why Eric could've been a great antagonist is mainly because Eric is essentially trying to do the same thing with Max. That made it personal, and in a sense, it could be rivalry between the two where Max is trying to defeat Eric. You are trying to counter everything that Eric did, and then turned it around to your advantage instead. That made it an interesting dynamic between the protagonist and the antagonist.
Your other alternatives had no such thing. Financial issue is a gameplay element with money that is so easy to make because there's not enough money sink. Cops looking for Eric's disappearance is completely one-sided and the cops are outsiders. Kate's mom is also an outsider that has no real interest in the family. Saving Kira from bad people has no real urgency because Kira is a secondary character. Drama in the house is the one that has the most promise, but seems lack of logic because Max becoming "successful" is a good thing for the family due to how they viewed him as a loser at the start. They might not enjoy how they depend a lot on him, but doing the opposite would also make it worse for them. So it doesn't make much sense to try to bring him down when it also brings them down with him.