The Multiplayer Modes seem to have a theme when you look over the options available in Categorization. Almost all of them include specific special cases for some form of Co-op or shared Split-Screen, but none for LAN Competitive.

The most obvious examples I can think of would be the GBA Link cables for local LANs such as the Sonic games, or the Ad-hoc/WiFi features of the PSP, 3DS and others where these aren't Co-op modes or Split Screen, but Linked and Competitive.