RAM speed makes a smaller difference in performance than the CPU or GPU do. The amount of RAM does make a difference, because RAM is there to keep from having to reread data from the much slower disk. The "TL; DR" version is RAM speed makes little difference in gaming unless the game is CPU-bound. Since most games are not CPU-bound, it usually makes little difference.
Actual RAM speed hasn't advanced much in years. Almost all the gains in RAM bandwidth have come from multiplexing and running more clock cycles per access. This gain becomes significant when you are running CPU-bound workloads. It is less important when there are other bottlenecks, especially the slower transfer over the PCI-e bus between system RAM and VRAM.
To analyze it more deeply, there are three transactions that dominate memory use:
CPU reads and writes between RAM and L3 (or L2) cache. The CPU doesn't read memory directly; it loads memory into cache, then reads the cache. Cache reads are in lines of 64 (sometimes 128 ) bytes. Because they're accesses to consecutive memory addresses, RAM is designed to allow these to be streamed at its full bandwidth. This is where, say, DDR3-1600 outperforms DDR3-1333 and why DDR4 is such an important advance.
PCI-Express reads and writes between system RAM and peripherals (especially GPU VRAM). These are also in long lines of consecutive addresses, but they're limited by the much slower speed of the PCI-e bus.
SATA reads and writes between system RAM and SATA peripherals (SSD, HDD). These are limited by the speed of the peripheral, which is many times slower than RAM even for SSD. It's important to avoid these as much as possible in high-performance systems. But because the speed of RAM is not limiting here, it's more important to have enough RAM and an operating system that knows how to use it.