I have Outlook installed only for reading legacy MSG files and their attachments. I don't even have an email account set up for it. (Very frustrating how Outlook just grabs settings!!)
In TheBat!'s Preferences I have all the options checked for "Associate TheBat! with specific file types/protocols".
This appears to be an Exchange web client. To access the messages via TB!, I think you need to set up an Exchange account with the OWA URL and whatever other requirements for that account, so you may need to contact that site administrator. I also have an Exchange email account and I can access mail either via the Outlook web app via a URL or I can access via an Exchange email account I've set up. Good luck, david