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You're right... if you consider Steam from about 4 or 5 years ago.
For the couple of last years, since Steam has updated its chart and tags system, there has been a specific tag for what you describe "Same system" local multiplayer/coop and, no, it's not a tag created by the community.
I'll post a link toward another game that has local multiplayer/coop so that you can see what is the official tag :
http://store.steampowered.com/app/448510/Overcooked/
Notice the "Shared/Split Screen" tag below the "Local Co-op" tag?
That's the tag you're talking about and Besiege doesn't have that official tag.
If it has networking it doesn't matter what kind of network it is LAN or WAN.
Adding "Local Co-op" tag just confuses people.