Is it possible to install Adobe Premiere Pro on a Microsoft Surface Pro X?

Unfortunately not. The Surface Pro X has an ARM-based processor (not Intel) which means it comes with some significant limitations.

One of those is that it cannot run 64 bit apps such as Premiere Pro. 64 bit apps have to be ported (re-written) to ARM64 to work on ARM processors.

From the Microsoft website: "At this time, Surface Pro X will not install 64-bit applications that have not been ported to ARM64"

https://www.microsoft.com/en-au/p/surface-pro-x/8qg3bmrhnwhk?activetab=pivot%3aoverviewtab

Lightroom 4.1 (Cloud), Photoshop (Beta) and Camera Raw are the only Adobe apps currently available for ARM processors.

https://helpx.adobe.com/au/download-install/kb/arm-processors.html

https://helpx.adobe.com/au/photoshop/kb/windows-arm-support.html

https://helpx.adobe.com/creative-cloud/system-requirements.html