My friend created his windows phone account to a yahoo address when he bought his phone. It doesn't HAVE to be a @hotmail/live/outlook.com to work. If op didn't have some credentials registered with Microsoft, he wouldn't even be able to buy apps.
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I didn't say he did. You can set up a Windows Live account using ANY email address but you DO have to have a Windows Live account in order to access Track my Phone. When you first set up your phone you're prompted for it. That's how you tie your phone to the account.
Also no where in the OP did it state he bought apps with his phone.
EDIT: After reading the thread again it seems we are talking about the same thing just using different terms. The OP said he didn't have a microsoft ID. He use ID, I use Windows Live and you use credentials. We're all meaning the same thing and he doesn't have one.