Not an option I’m afraid. Steam games strongly dislike trying to run on an NTFS formatted drive in Linux. This had me stumped for months until I sat and had a think about it one day, then it dawned on me to try using ext4 instead. I went from having no working Steam games, to most of my 1000+ catalogue working via Steam Play without issue 
I reckon it’s something to do with the need to run through the NTFS driver that causes Steam games to bomb out immediately on launch (regardless of game), but on Ext4 they work perfectly.
If you want to share a library between Linux and Windows, personally I’d recommend exFat, as it has native support in both OS’s.