Maybe it's because I am using the "new" Outlook
Not necessarily. It should work in both the old or "new" Outlook...
If you have exchange accounts - msn, hotmail, live - you can move mail around.
But...
If you have gmail added as a 'Microsoft cloud account' moving mail may not work, unless you are moving it out of the account.
If the gmail account has the google icon, it uses the cloud. I don't recall if it says "Microsoft sync technology" in the new outlook, but that would indicate the cloud, not IMAP. If you remove the account and add it back as IMAP, moving show work. After outlook find the account, you need to click Not Google to select IMAP.