No, IMAP, POP3, and SMTP are not APIs.IMAP and POP3 are API to access mailboxes.
SMTP is an API to send mail.
They may still sue for damages, if their contract allows for it. Unfortunately in the meantime, Twitter has destroyed their ability to operate their products for their users, revoking their agreements without warning under literal cover of night.
I agree that the communication was terribly mismanaged. But I think it was the right business decision long term.
I doubt these other companies have any grounds to sue, considering by using Twitter's API to begin with they had to agree to Twitter's terms of service, of which I have zero doubt included language that says Twitter has the right to change their terms of service at any time and without notice.