I know it probably slows down the network for the ones that are engaged in the LAN multiplayer game because the packet queue gets filled up, but does it affect other users that are accessing the internet?
Go to WiFi near the bottom of the message, bellow is some stuff more related to protocols and wired connection.
If the Internet Protocol is used, some congestion may occur ONLY if the game is using UDP/broadcasting for the multiplayer, as broadcasting means a packet is sent to all the computers in the network.
If IPX/SPX is used, then it also depends on the implementation. The only experience I had with this was in Bomberman, which definitely used broadcast => packets sent all over the network (routers went nuts - Internet was available, but routers thought it was some kind of attack LOL).
Overall, I would say that the chances a LAN party chokes the Internet connection are fairly slim, if the LAN has proper switches.
What could go wrong:
Edit: Oh, WiFi, got confused by the "hubs" post...
For WiFi, it depends:
If the WiFi transmitter is the Router, it could cause latency for the Internet connection. It very much depends on the router's capability: how many computers can be connected at the same time (number of wireless frames or fragments), can it prioritize packets.
If the WiFi transmitter is independent from the router, then, it shouldn't be a problem for the devices connected by wire or through another wireless transmitter. If they are using the same WiFi, then you get the same thing as for the WiFi router.
So, for WiFi, yes, if there are many computers, much traffic from the game, and surely if the WiFi is also secured.
In my experaince it depends on the game. Most games don't use a lot of traffic compared to streaming internet video but If you want to get technical I would recommend this paper, they cover the topic in detail.
In essence, bandwidth varies per game. The paper covers network usage during tournaments of three popular First person shooters. They concluded that the maximum bandwidth needed per client was no more than 1600Kbps, which any modern household router can handle without affecting internet usage. Assuming your not maxing out the routers capacity.