A free program available for Windows, Mac and Linux is Open Broadcast Studio which will record screen activity. It creates conventional video files, which you would then resize for your screen purposes.
Your objective is a bit unclear, as you've not indicated what program you would use to display the video. There are stand-alone video players such as VLC player which will play the OBS-created files.
Note that the above referenced program can also be used for live streaming, and much of the material is presented from that frame of reference.