Those three words have something in common.
People have coined words like "chocoholic" and "shopaholic" that mean addiction to chocolate and shopping, not chocohol and shopahol.
People have coined words like "cheeseburger" and "mooseburger" that don't mean a food item originating from the cities of Cheeseburg or Mooseburg.
People have coined words like "Nipplegate" and "Strippergate" that refer to scandals that aren't related to a hotel called Nipplegate or Strippergate.
I'd be amused to learn of other examples. I'm not sure if there's much more to say in terms of what's going on behind the scenes. I guess in each case, after the original word became common, it got reanalyzed in the popular imagination. "Alcoholic" got reanalyzed as "alco" + "holic", "hamburger" got reanalyzed as "ham" + "burger", and "Watergate" got reanalyzed as "Water" + "gate".
So then people associate the suffix "-holic" with addiction in general, people associate the suffix "-burger" with patties on a bun in general, and people associate the suffix "-gate" with scandal in general, even though doing so isn't "true" to the etymological history.
And by the way, it would be kind of silly to say that therefore coinages like "chocoholic" are illegitimate or wrong. It would be a little like saying the expression "the algorithm" is wrong because the "al" in "algorithm" historically comes from a definite article, making the "the" redundant.
Or, at the very least, the time to object to "chocoholic" would have been when the word was first being used. Now that it's caught on, it's too late.