Anything you are doing which involves shoveling data is faster with 64 bit because more data is shoveled per shovelful, plus you don't have register starvation. When amd64 was new it was typical that doing absolutely nothing but recompiling the same code as 64 bit could produce a 10-15% speedup in CPU-limited software. This is why the X32 ABI is so interesting for smaller programs which don't require large address spaces but could still benefit from the overhead reduction from processing 64 bit data types, and the fact that amd64 has genuinely general purpose registers— and a lot more of them than x86.
In the real world, ideally you hand video encoding off to something that's better at it than the CPU. Mainstream video processing software has been GPU accelerated for a long time now, and GPUs also handle the video encoding. For example with Nvidia, NVENC uses DMA and so does your storage device, so in a fully accelerated encode path there's no CPU instructions involved in any of the actual encoding parts and it's mostly directing traffic, unless there's encryption involved. Even the limited number of GPU cores in a typical embedded GPU can give good video encoding performance.