Trust me you don’t want the smoke here: the phrase “Familial NTR” is a reconstruction of the concept of NTR as it commonly appears in many manga. Though it involves a reference to the sexual nature of NTR, it is mockingly NOT sexual in nature.
By this standard it means a common situation where a member of a family stakes a love for another member to some exaggerated degree, and this is due to their longstanding and usually reciprocal relationship. E.G. the father who dotes on his daughter and gets hit with the “I’m going to marry Daddy” line; The sibling who wakes up their other by slipping into their bed in the morning and then asking for a kiss; The cousin who sees their older cousin only once a year but devotes nearly all of their time and has dreams of “when I get bigger I’m gonna make you notice me”.
This is then brought down by the introduction of some “other” character, usually the MC, who is capable of having a normal relationship with the person in question, but the doting family member CANNOT stand to have that happen despite it happening regardless. Often played for laughs this goes about having arcs where the “other” in question is either threatened, or tested, interrogated, or stalked etc. The hyper-intense reaction of the family member along with the clear intention of the author that no serious relationship is occurring makes for laughs and the inclusion of many suggestive lines for the sake of comedy. The key here is that in this context it is clearly COMEDY, and I’m expressing my distaste for this style of comedy: Familial NTR.
If you look at that last image of a woman on a man’s lap who is clearly smitten with the man while the “loser” cries out in agony and it doesn’t elicit hundreds of that same image or concept, then YOU need to read more NTR and understand the expansion of the word and associated phrases.