No. The English used around the world is not a "pidgin" and was not "developed from a mixture of two or more languages" in the sense described in the definition of pidgin.
The English used around the world is an adaptation of the native English spoken in countries such as the UK, US, Australia, Canada, etc.. Some countries such as India have adapted it as a national language to be used alongside indigenous languages.
There are separate definitions of languages used for communication among various people. Technically, in some areas, English might be a Lingua Franca, a creole or a koine, but in most uses, it is simply a dialect.
I understand much of the English/African creole, Gullah, but I usually do not attempt to speak it.
I think the pidgin used in New Guinea combines English with other languages, but it is hardly "used around the world."
I believe the use of English by other countries is voluntary except in international aviation where it is mandatory.