Personaly i don't have a theory, i simply don't care enough to bother about it.
Yeah, it would be the most boring and mundane relevation there is...but what do you expect will come out of it ?
If we take the MC's normal behavior.
He will most likely run out of that bar (runing away and making his own headcanon is his thing), then he will go full on drama queen, like always...of course he could just wait a minute and ask Alexis for clarification, like most normal people would do...but that would be too boring for Nyx.
Either way, Santi in the bar is pretty surely MC's father, so he isn't Alexis dad either by blood or by law.
I mean, Santi could be the boyfriend of Adriana, living with them and raising the kids for so long Alexis started to call him dad and now he wants one more kid with Adriana...but that they never married under these circumstances would be even stranger imo, add to that why there was that big picture of him and Gabi over her bed.
What other reason could there be for Alexis to call him dad, if we exclude them being related and of that we can be sure.
As a nickname ? Would be a bit too strange, well maybe if they are up for some naughty roleplay