Term for words like Snowmageddon, Nipplegate and even cheeseburger?

Solution 1:

This sort of portmanteau is closely related to the phrasal templates called snowclones:

Snowclone is a neologism for a type of cliché and phrasal template originally defined as “a multi-use, customizable, instantly recognizable, time-worn, quoted or misquoted phrase or sentence that can be used in an entirely open array of different variants.”

An example of a snowclone is the phrase “grey is the new black,” which gave rise to the template “X is the new Y.” X and Y may be replaced with different words or phrases—for example, “comedy is the new rock ’n’ roll.”

You could probably call such a word a snowclone and be understood, although if you want to emphasize that it's a single word, you could call it a “snowclone word” or “snowclone portmanteau.”

Solution 2:

I don't know if this is quite the term you're looking for, but you could refer to such clever wordplays as abstractions.

Etymonline says, under its entry for -gate:

-gate: suffix attached to any word to indicate "scandal involving," 1973, abstracted from Watergate...

I wondered if that was a one-time mention of the term abstraction, or if it was used at other places on the site, and I found similar phrasing under entries such as -aholic, -rama, -fest, -athon, slimnastics and yes, even cheeseburger:

-oholic: word-forming element abstracted from alcoholic; first in sugarholic (1965), foodoholic (sic., 1965); later in workaholic (1968), golfaholic (1971), chocoholic (1971), and shopaholic (1984).

-rama: noun suffix meaning "sight, view, spectacular display or instance of," 1824, abstracted from panorama (q.v.), ultimately from Greek horama "sight, spectacle, that which is seen."

-athon: word-forming element denoting prolonged activity and usually some measure of endurance, abstracted from marathon. E.g. walkathon (1931), skatathon (1933); talkathon (1948); telethon (1949).

slimnastics (n.) 1967 (with an isolated use from 1959), from slim (adj.) + ending abstracted from gymnastics.

cheeseburger (n.) 1938, American English, from cheese (n.1) + ending abstracted from hamburger.