YES, IT DOES!
StrokeIt works in Windows 10, all you have to do is right click its exe file (folder installation) and choose troubleshoot compatibility. Follow the steps and set it to Windows XP sp3 mode. Now you should be able to run it correctly but you're going to deal with another problem: it's under UAC warning now for every time you start it.
You can solve that too. Just create a startup schedule task for it. If needed, here is a similar exemple for how to create a task to run a program at startup: http://www.sevenforums.com/tutorials/67503-task-create-run-program-startup-log.html . The "Configure for:" item on General tab can be as Windows 10. The ruler is the already Windows XP choice you took before. Of course you can try that skipping tne compatibility step and check Win XP on the scheduler. I did it here using the two steps (from Win 10 Pro x86).
And yes, Strokeit is supposed to be resident in your system, and it is a perfect program for that, only 0,1MB of your memory.
For another solution, using .VBS, easier or not, it's up to you, read this here: "Taskbar icon fix fails with Windows 10" by MKairys http://www.tcbmi.com/strokeit/forum/read.php?2,58767
