In case anyone comes across this: I was having the same issue when I fired up a fully-updated Shenmue I and II last night and for the first time on a 4k monitor, and it does seem to be related to the scaling. Right click on the app, choose the Compatibility tab, choose Change high DPI settings, choose Override high DPI scaling behavior, and set Scaling to Application. That seemed to fix it for me!
Apologies for responding to a super old post, but hoping it's okay because it's pinned. I was trying to find this information here and around the web and had no luck, so I thought it would be good to have a record of it somewhere!