According to SWTOR Customer Service, the developers originally thought that the Win10 was an isolated incident but have finally received enough reports of issues to now begin trying to find a workaround or permanent fix. So to the folks the game is working for with Win10 cool but please don't assume there isn't an issue. Also, they were clear on the fact that they have no ETA for said solution at the current date. All I can say is if you have done all of the below, report the issue in the forums ASAP:
1) Gone through and verified you are not on an earlier version of Win
2) Unistalled and Re-installed the game
3) Updated DiretX Drivers
4) Done the repair install option on the launcher settings and still the launcher blips out
5) Verified all files recommended in the original Developer workaround post are corrected
6) Rebooted computer and game
Please report your issue. Having an even clearer idea of the total people affected may push for faster fixes.