Shoutbox

It works properly with all those other programs because all of those other programs are fully-fledged POP3 email clients. They download all mail out of your Gmail account, and create a local copy on your computer, which is presented to you for you to read and manage/delete. Normally, with POP3 mail, once a client downloads messages, it deletes from the server. Gmail won't let the client do this, but you can set Gmail to take an action with downloaded messages. You then read them in the client, you delete them from the client, or the client marks the local copy as read.

Messenger Plus! is not a email client. It reads the POP3 data from Gmail, and reports the number of messages. If you choose, Messenger Plus! will launch a full POP3 client, or open www.gmail.com in your default web browser when click your email notification.

That list exists because they are popular programs, and Google has had the time to create step-by-step guides to entering Gmail's POP3 settings into them. It is not a supported clients list.

Edit: Spelling and clarification