Assuming they do wish to maintain interoperability, you can use matrix while extending the base "events" that are sent to clients. So it may be that essentially Teamspeaks client/server will support the main specification "m.room" events, such as joining, leaving, adding/editing titles, etc, while also exposing their own "com.teamspeak.event" addons (which might be invites to voice channels or recordings or something specific like that), which so long as the client says "oh hey, I know those, speak them to me" will work fine, and any other client could still get the basic chat functionality.
I'm not sure how exactly this works with server <-> server federation, I've never actually looked at that spec.
Reminds me of Jabber and how GTalk was first able to talk to anyone out there before they locked it down with their custom modifications to the protocol.
