A 1 Gbit/s connection is a great bandwidth (you probably mean 1 Gbit/s and not 1 GB), bit the latency is even more important. If the game movements and actions lag behind your physical input, this can ruin the whole experience, no matter if the stream has a great quality (few compression artifacts, high resolution) thanks to the bandwidth.
I only used the Shadow gaming VM service so far and the servers are in a neighbouring country, with 100 Mbit/s bandwidth and 30ms ping to 1.1.1.1, so not optimal conditions, but GTA IV, Minecraft and other games were not fun to play due to the input lag.
This all depends on where you live and the infrastructure. I have 1 Gbit fiber, but in my country nearly all the infrastructure is concentrated in one of 2 cities, so I still have minimum 15/30ms (IPv6/IPv4) ping to everything since it has to travel across the country.
I only used the Shadow gaming VM service so far and the servers are in a neighbouring country, with 100 Mbit/s bandwidth and 30ms ping to 1.1.1.1, so not optimal conditions, but GTA IV, Minecraft and other games were not fun to play due to the input lag.