'-gate' as a suffix to coin words related to scandals and corruption cases

All these formations are modeled after the Watergate scandal which you mentioned. That scandal, in turn, took its name from the very innocently named Watergate Complex, a group of buildings in Washington DC which happened to house the office which housed the documents that were stolen as part of the Watergate Burglaries, and thus ended up giving its name (or at least half of it) to various political scandals for nearly half a century since.

The suffix itself doesn't have anything to do with scandal, intrinsically. It's the association with the famous Watergate scandal that gave it its new meaning.

As other answers have noted, the first scandal ending in "-gate" was the Watergate scandal.

The Oxford English Dictionary says that other scandals having "-gate" tacked on happened reasonably quickly:

Only a year after Watergate, the scandal had become so well known that -gate became detached and was used to create names for other scandals. The OED’s first recorded example is from August 1972 in National Lampoon:

‘There have been persistent rumors in Russia of a vast scandal... Implicated in “the Volgagate” are a group of liberal officials.’

A few months later the -gate craze had shown no signs of abating, a fact signalled by the weary use of ‘inevitably’ in the following quotation:

‘Inevitably, the brouhaha of Bordeaux became known as Wine-gate.’