This is a traditional game called "Voyna Virusov" or "Virus War". There is a version of it on Pencil and Paper Games with clearer rules, and some background history:
Glad it wasn't just me. I found them challenging to grok due to their complexity and lack of clarity in key aspects such as movement, grid layout, and strategic objectives.
*The fact that the pencil symbol controls the number of moves per turns, which was 3 by default, confused my learning process for a good 10 minutes as I had no idea what was going on.