These are the older PC games I keep on my cockpit which are LAN-capable (none of these are very arcade-like, though):
rFactor - with all of the mods which tend to be full conversions, I consider this a many-games-in-one option. This is, however, way over on the sim side of the spectrum, which doesn't seem to be what people in this forum are interested in.
Rallisport Challenge - supports up 4 players over LAN.
Cross-Racing Championship - supports peer-to-peer connections, but I don't know how many connections it can handle.
GTR2 - supports peer-to-peer connections, but I don't know how many connections it can handle.
Flatout 2 - I believe this supports 4 players over LAN
Race Driver Grid - can support 4 LAN players