Hey quick fix I found for this issue for everybody running this game on a computer with no disc drive to use, because Pajama Sam 4 Life is Rough has the same issue:

Download DAEMON Tools Lite off the internet (it is both safe and free if you don't get the subscription) and create a virtual disc drive.
https://www.daemon-tools.cc/products/dtLite
Keep the Drive running, and open Putt-Putt normally.

For some reason that I think has to do with a change in the game engine they use, the newer HE games exe file relies on a disc drive to run, and refuse to work without it. I don't really know what's up with that, why it works that way and can't just access it directly, but yeah, just get yourself a virtual disc drive and Putt-Putt should behave normally. Another Perk of this method: You don't have to go crawling around through game files and possibly messing up on a copy-paste. This DAEMON Tools method worked for Pajama Sam, and I tried it with Putt-Putt and the same thing works, on a Windows Surface running 10.

Happy Putt-ing everybody!