You've linked competing hardware encoding APIs which are not x264/x265.
x264/x265 are software encoding libraries for H264/H.265 video formats and don't really use hardware acceleration beyond SIMD instructions on CPUs. x264 is known for its great output quality while still being fast on x86 CPUs.
x264 and x265 refer to the specific set of software programs of the same name, right? Most chips nowadays can hardware accel H.264 and H.265, but they don't use x264/x265 (or do they? Not sure...). I think the confusion is that the terms x264 and H.264 are not interchangeable
This is incredibly false.
https://en.wikipedia.org/wiki/Intel_Quick_Sync_Video
https://en.wikipedia.org/wiki/Nvidia_NVENC
https://en.wikipedia.org/wiki/Video_Coding_Engine (this has been widely available for 8 years)