Swapping contiguous regions is sequential, and Windows will preemptively write non-locked regions to disk so it can instantly discard them when needed. You can force this behavior by dropping working sets, which has the effect of "converting" used RAM to cached pagefile.
Of course if you're actively using a program, it will swap out other processes, that's the whole idea.
It doesn't make sense to swap out other programs just to load video that will be immediately discarded after displaying. It makes more sense to have limited download and playback buffers and store most of video data on the disk.
> and as long as Chrome doesn't lock the memory range, the OS will swap it to disk anyway
Swapping in/out is random access and is very slow (< 1 Mb/sec) compared to linear reading/writing unless you have SSD.