Firefox and Chrome explicitly block ANY playback in the HEVC codec. No software decoder, and it won't pass off a HEVC bitstream to a system level decoder either. This was a business/political decision. Older builds of Chrome and Firefox did support bitstream passthrough of HEVC, just like they do with H.264, until they added explicit blocks. It's pretty trivial to remove that limitation in a Chromium build, which Edge has done.
Microsoft's game streaming technology is based on HEVC, which is a particularly good codec for this kind of content. It has tools that allow for low bitrate encoding of sharp edges without artifacts. As YouTube constantly demonstrates, games are full of sharp lines and single-pixel details that do not encode well in traditional video codecs that work only in the frequency domain. Without HEVC, bitrates and latency would be quite a bit higher and quality would be lower.
Safari and Edge DO support HEVC if the underlying system has a decoder, which is why XBox Game Streaming can work on Safari.