G-Sync and FreeSync are Nvidia and AMD's kind of proprietary version of v. sync. If you have a 60hz monitor and your display is putting out 50 frames per second due to demand (games), the image can "tear". It looks like there is a literal tear in that particular frame. What FreeSync and G-Sync do is sync the framerate of the monitor to the framerate the computer is outputting, preventing the tear. Both systems work remarkably well from what I have seen. In order to work, the GPU and monitor both have to have support for the respective standard.
I do not believe Apple supports either standard. And even if they did, it really is meant for gaming and not much else as far as I know. Further, there is a cost associated with FreeSync and especially G-Sync (G-Sync is a large premium), so you really do not want to pay for that feature if you will not use it. Having said that, it is mostly on gaming centric monitors which are unlikely to be the best choice to pair with a Mac. The monitor you reference is a gaming monitor. While it is a very highly regarded monitor for gaming, and I *think* pretty good monitor overall (it is an IPS panel), I don't think it would be my first choice unless I was gaming a lot and had an Nvidia GPU.
[doublepost=1543211211][/doublepost]
I have one anecdote to share about the Mini and an Asus G-Sync monitor: one poster in these forums could not get the combination to work correctly, at all. My guess was that the G-Sync hardware was confusing the enumerator in the device driver for the Intel iGPU.
Based on this single anecdote, I'd suggest:
1) Bringing the monitor to a Mac store and plugging it in to a Mini to be sure it will work at all
2) If it does work, the Mini's iGPU does not support g-sync, so:
3) Yell at Apple and NVIDIA, like many of us are, to get Mojave drivers released so that we can use modern, G-Sync capable NVIDIA GPUs as an eGPU with our Minis
I am pretty sure G-Sync does nothing at all if there is no G-Sync compatible GPU connected. I could be wrong, but I was under the impression that the feature is simply dormant without both ends (GPU and monitor).