Why do these three games have LAN play as an option?
These games offer LAN (wired connection) for multiplayer (source below).
Games like Mario Kart 8 Deluxe and Splatoon 2/3 also offer LAN play. Those make sense to me. Those games are capped at how many players you can play with per system (MK8D being four, and Splatoon 2/3 being capped at one), but they offer multiplayer modes with more than those caps (MK8D being twelve and Splatoon 2/3 being eight). Of course to
play a real match of splatoon you’ll need 8 systems and 6 for Mario Kart since LAN play is capped to 2 players for Mario Kart.
But these other games? They seem to have 4 player options baked in, and I can’t find any info online about playing any modes with more than 4 players
The box art can be deceptive as MK8D’s box art shows 1-4 players but as previously discussed that’s not the whole truth.
Links to official resources from Nintendo to access these modes:
NS Sports https://en-americas-support.nintendo.com/app/answers/detail/a_id/60488/~/how-to-use-the-lan-play-feature-of-nintendo-switch-sports
Mario Maker 2 https://en-americas-support.nintendo.com/app/answers/detail/a_id/47650/~/how-to-use-the-lan-play-feature-of-super-mario-maker-2
ARMS https://en-americas-support.nintendo.com/app/answers/detail/a_id/26390/~/how-to-use-the-lan-play-feature-of-arms
MK8D https://en-americas-support.nintendo.com/app/answers/detail/a_id/25961/~/how-to-use-the-lan-play-feature-of-mario-kart-8-deluxe
Splatoon 2 https://en-americas-support.nintendo.com/app/answers/detail/a_id/27035/~/how-to-use-the-lan-play-feature-of-splatoon-2
Splatoon 3
https://en-americas-support.nintendo.com/app/answers/detail/a_id/59460/~/how-to-use-the-lan-play-feature-of-splatoon-3#:~:text=Main%20Square%20menu-,After%20entering%20the%20Shoal%2C%20press%20and%20hold%20the%20ZL%20Button,few%20seconds%20if%20done%20correctly.