I have not loaded version 10 on Sierra OS. However, version 10 should run on any version of OSX -- and quite likely Sierra also. The basic code of the OS isn't that different.
Version 10 is, however, a pretty primitive version of Premiere Elements. It requires you to manually set up your project files to match your video and, if you set up the project wrong, it can mess up your entire project. (Version 11 and later set up your project automatically.) It also edits pretty much only digital camcorder video well. You don't say what your video source is, but if you are editing video from a smartphone, GoPro or any current camcorder, I'd highly recommend you upgrade to at least version 11 (or better version 12, so you can at least run a 64-bit version of the program -- otherwise you won't be able to take advantage of more than 4 gigs of RAM).