It's likely that whichever program you see receiving mail in "real time" is using something similar to IMAP's IDLE command (http://en.wikipedia.org/wiki/IMAP_IDLE).
"The IDLE feature allows IMAP e-mail users to immediately receive any mailbox changes without having to undertake any action such as clicking on a refresh button, or having the e-mail client automatically and repeatedly ask the server for new messages."
With this, the client establishes a connection and asks the server to notify of any incoming email, leaving the connection open at all times. When an email arrives, the server notifies and the client can take action instantly.
This feature is NOT supported by POP3.
My guess is that Outlook uses some proprietary protocol to communicate with Live (or whatever), which supports a similar feature. Outlook is most likely not using POP3 to connect with Live.
So to answer your question "Is there any way to receive email in "real time" without using a web browser?". The answer is "YES" given proper support of the required features on both client and server, and compatibility between them.
Look at whether Live supports IMAP, then check whether your mail client supports IMAP IDLE, if so they may be able to work together and do what you want.