So a few weeks later PG running OK on Mint 19.1, 4.20.7 kernel. A few things I'll throw out there..........
Installed the new Wine 4.0 stable release. Not sure if/how Steam/Proton interacts with it but no issues since I installed it 10 days ago.
Graphics- I play PG at 4K resolution, RTX 2080Ti using the 415.27 nVidia driver. The graphics are pretty good but not quite as good/sharp as they are in Win 10. Overall detail just isn't quite as sharp. Have played with all the ingame settings, figure it's just how the video card/driver & Linux work (or don't) together. One issue is the fairway in the overhead always shows as black. Toying with picking up a Radeon VII card to compare as AMD drivers are supposed to be better in Linux vs nVidia for gaming.
RTSM- In Windows you have 3 layers to your mouse- the Windows settings, your mouse software settings and the PG settings. In Mint it's just the Linux mouse settings (which are just Acceleration and Sensitivity) and PG. But it seems to be harder to achieve a fluid smooth motion. I have Acceleration set at 75% and Sensitivity at 15% on the Linux sliders (which works great on the desktop and programs), 3.1 and 3.7 in PG's settings. But to get a fairly straight shot off the tee or fairway I have to use a really fast back/forward motion , literally 1 second total where as in Windows it's a 2 second back & through. The fast swing in Windows gives me a pull every time, the 2 second motion in Linux gives me the pull every time. I've gotten used to it but it took a lot of trial & error to get it usable.
Haven't tried 3-click or controller (controller does work on TGC2019 under Linux).
PG loads so much faster in Linux vs Windows. Like 5-7 sec in Linux, 25-30 in Windows. Courses load a tad faster as well.
Overall I'm happy with how PG works under Linux.
Desktop- ASRock Fatal1ty Z370 Gaming K6, i7-8700k, Corsair Hydro H150i Pro cooler 32Gb DDR4-3400, EVGA RTX 2080 TI XC Hybrid, Samsung PM981 1Tb NVMe & 850 EVO 1Tb, Adata 960Gb SSDs & Hitachi 3Tb HDD ,EVGA 1000w G1+ PSU,Monoprice 27772 32" 4K HDR monitor x2,Windows 10 Pro x64, Linux Mint 19.1
Laptop- Eluktronics (Clevo) P670RS-G i7-6700HQ, 16Gb DDR4, 512Gb & 256Gb NVMe SSDs, GTX 1070 8Gb graphics, 17.3" 1080p G-Sync, Win 10 Pro x64, Linux Mint 19.1
XBox One X 1Tb w/2Tb external HDD, PS4 Pro 1Tb w/1Tb external HDD