Probably not.
Wine is not specific to Ubuntu; it will run on most Unix-like OSes and virtually all GNU/Linux systems. Wine can run on SteamOS. (SteamOS is actually not that dissimilar to Ubuntu--both are derived from Debian. But Wine came before Ubuntu and runs fine on systems that are quite unlike Ubuntu, too.)
Therefore, if a game needed Wine, it could simply use Wine on SteamOS or any other GNU/Linux OS. Having access to an alternative implementation of DirectX wouldn't prevent Wine from being used; if a game worked better with Wine, it could simply use that instead. Each game could ship with Wine (whatever version worked best for it), or Wine could be included in the platform.
You might be thinking that using DirectX DLLs taken from a Windows system, using Wine would be more effective than using an alternative DirectX implementation (such as the OpenGL-based port that you mention Valve is developing). After all, Microsoft DirectX can be installed in Wine, and many gamers (including many Ubuntu users) do this on their regular PCs.
However, distributing Microsoft's DirectX implementation(s) in this way--as part of the underlying platform or together with a game--would likely violate Microsoft's license. Note that I am not a lawyer, I could be wrong, and this is not legal advice even if I am not wrong. Furthermore, DirectX doesn't work perfectly on Wine currently and future versions (even minor updates) can't be relied on to continue working as well as existing versions do.
A related but different possible solution comes to mind: Traditionally, gaming consoles don't have to keep track of much state between games, and are able to start up and shut down very quickly. For a console intended to run only Windows games, it seems likely that Windows Embedded would be a technically appropriate choice of platform (though it is not free open source software, the platform vendor would have to pay license fees to Microsoft, and I'm not sure whether or not current licensing schemes for Windows Embedded would facilitate this sort of deployment). For a console intended to run games that are available for GNU/Linux or can be ported to GNU/Linux with reasonable effort, a GNU/Linux system would likely be most appropriate. The natural synthesis of these needs would be a dual-boot console, which simply boots into whatever OS is needed by a game. If the platform were to support concurrently running non-game applications, they'd probably be more portable and could have a version for both OSes, and otherwise, they'd probably not be graphically or otherwise resource intensive, so virtualization could be used.
