Yea, unity tries using OS media codecs for the video player component, maybe Wine works better, idk I don't have linux.
I tried another game also made with Unity. Purah’s Lab. It has same thing with video, screen is blank and no sound. However, the video files are mp4 and in subdirectory of game folder. Those files played just fine with command mpv, video and sound. So there is codec for them on my Ubuntu 22.04.
I do not know how Harem Party tries to start the video nor what file format they use, but it may be some small thing that would be easy to fix running Harem Party under developer tools or debugger.