Right, thanks hmhealey. It turns out our intranett (mycompany.com) is configured to run in compatability mode by the group policy.
In the first picture you posted, "Display intranet sites in Compatability View" is not ticked, but it is actually greyed out.
When I got into F12 developer tools, Emulation, the user agent string is "standard" (not IE 10). But when I change it to EI10 and reload the page, compatability mode gets put back on via the group policy.
I guess I need to talk to my admin about allowing "chat.intra.mycompany.com" to NOT be forced into compatability mode, even if "mycompany.com" sites are forced to.
(unless you know a way to force override for a specific site, locally in the browser, to override the group policy and turn compatability mode OFF ??)