What are key things to be looking for in a gaming system?
The most important thing to focus on is the graphics card, within reason.
Most modern CPU's are capable of feeding the required data through to the GPU. With higher resolution gaming, you are even more GPU bound and a CPU will not make much difference at all.
Of course it can be nice to future proof the system for productivity workloads that take advantage of more threads so hey, if the budget permits, by all means look at the Ryzen 5800X, modern i7 or better.