If a person addicted to alcohol is an alcoholic....

…why isn’t a person addicted to work a workic-instead of a workoholic? or a person addicted to chocolate a chocolatic? Or maybe we should say a person addicted to alcohol is an alcoholoholic.

Because chocoholic, workoholic, etc., all started out as slang/coined terms. The anonymous creators of these words were deliberately trying to evoke alcoholism, and the connection is more clear if you use the whole “-oholic”.
Sometimes this evocation tendency goes overboard. I for one hate that Watergate came first amongst our major scandals. I despise “Monincagate”, “Travelgate”, “Contragate”, etc. My personal favorite of recent times was “Iranamok”, but it lost to “Contragate”.


Another reason, for 2 cents.
The origin of “alcoholic” is not from “alcohol” (the adj. is “alcohol” like in “alcohol solution”, not “alcohic solution”), it’s from “alcoholism”. Of course, there is no “workism”.
So, the real question should have been, why not “alcoholist”. Another “-ic” I know of is melancholic. Does mechanic, n. belongs here? Asthmatic? Diabetic? Fanatic?
Will it fill your Sunday?