According to that definition, you're wrong: Mailchimp doesn't fulfill the first condition. In my experience, Mailchimps interface puts heavy emphasis on having opt-in proof for the addresses you use, having to include unsubscribe links and sender's postal addresses etc. Yes, they don't technically enforce it, but how could they do that without also preventing legitimate use cases like importing addresses from a competitor's service?
If they gave you enough info to opt out effectively, people would do it. Also, then people could check up on them, checking the list of claimed "opt ins" for spam trap addresses. Giving the user that access would allow users to definitively catch spammers and mailing services in lies, and could lead to prosecutions under the CAN-SPAM act.
No. After a transaction is complete, any further communication from the seller is spam. MailChimp treats a previous transaction as a license to spam. MailChimp says they're in the "email marketing" business and writes about "campaigns". That's spam.