"Tschüssikowski" is a somehow humorous version derived from "Tschüss" which simply means "Good bye".
I don't know if there's an official name for transforming a common "standard German" word or phrase into something theoretically senseless that however sounds similar enough to the original to be recognized, but that is what has been done here. Sometimes it is done by mixing unrelated words together or appending unrelated endings, sometimes there are just some twisted letters, sometimes an entire word from a different topic is used instead of a similarly sounding one ("Malapropism").
Such humorous phrases were somehow quite popular in the past (before my time, maybe in the 80s), but is considered pretty annoying by most people nowadays. From my perception it's no longer really commonly used, except maybe by a few people who conserved that kind of humour.
Some more similar examples that belong to the same category IMHO:
- zum Bleistift (zum Beispiel)
- bis Baldrian (bis bald)
- Wirsing! ([Auf] Wiedersehen!)
- Schlepptop (Laptop)
- teflonieren (telefonieren)
- Schankedön (Dankeschön)
and so on...