Was Twitter ever part of that group? I thought it was Google, Facebook, Microsoft and Amazon.

Last time I heard the expression it was Netscape, Oracle, IBM and Sun (vs Microsoft). I wonder how the OP would feel about working for one of them now.

+ Apple

Everyone always says four, yet swap Apple and Microsoft... This is apparently for historical reasons—there's always been a "big four" since the Great War. https://en.wikipedia.org/wiki/Big_Four

It's clearly currently five. In order of market cap: Apple, Alphabet, Microsoft, Facebook, Amazon. Note that these are now the five biggest publicly traded companies in the world, not merely in "tech" (a clearly archaic categorization).

I was about to write that you are wrong because how could Facebook and Amazon be on that list. But you are right. All oil and gas, conglomerates, pharmaceutical, financial services, electronics, retail, commodities, telecommunication, utility and automotive companies that crowded the list until recently have been displaced by IT companies. It is truly stunning.

The reason people typically don't include Apple is because they are diversified out of software, whereas Google/FB/Amazon/MS are all software tech companies.

This isn't exactly a strong line though, since all are at least diversified into things outside software.

Nevertheless, that was the original reasoning.