That dock product is built around a proprietary technology called "DisplayLink" (note: DisplayLink is very different from DisplayPort). DisplayLink requires you to install a proprietary graphics driver on your host computers so that the output of the computer's GPU can be compressed with the proprietary DisplayLink codec so it can be sent over USB 3.x to the DisplayLink chip in the dock which decompresses it and sends it out over HDMI or DisplayPort.
As to whether the DisplayLink technology in general, or the specific DisplayLink chip in that dock in particular, will support 144Hz and G-SYNC is a question for the product vendor. DisplayLink is proprietary and not well documented publicly, and I believe the technology has evolved over time, so there's no easy way for outsiders like us to say exactly what that product is capable of. You need to ask the vendor.
In general, even the folks behind DisplayLink don't recommend it for anything more than "casual" gaming. So since you're asking about 144Hz and G-SYNC like "serious" gamers tend to do, it's probably not the product for you.