Now that you mention it, on win 10, on first swtor boot it installed an old DirectX version, but couldn't see which one.
Gotta love it, that the game needs such old version and doesn't run on the newer ones.
Yeah, but it is actually a lot more complicated and before I go type out a whole essay again, you might find this link interesting that will explain why you have to re-install the distribution and also the effect this have on network packets etc etc. All in all why it plays such a huge part in things people see go wrong with their BOT (BW) and blaming the BW devs when it is actually not. hah and other times (like now) I *DO* blame the devs for changing things server side and BW not working as it should!

That aside, if you are interested you can google with keywords swtor, directx9 and win10. Aside from that, if you are unfortunate enough to have a more modern graphics card as in my case the Nvidea 980, you will more than likely have to tweak those drivers as well, since the latest Win10 drivers also allocates and use memory different which also plays havoc with BW. Aaaarg lol
Anyway - link as promised:
https://xnagamedeveloper.wordpress.com/2012/08/23/swtor-and-graphics-part-2/
And Wired, yes swtor checks and sees the new Win10 DirectX simulation as "true" and installs a couple of things but it is not the whole story.