This section of the forums was created way back before Gemp. People were playing online but there was no support for leagues, so they planned games and kept track of wins and losses here to determine winners similar to how it might've been run in person. Now there's not much need since Gemp does this sort of thing on its own.
Leagues are manually created by league administrators, which are the people with + before their names in chat and most everyone with * before their names. There are three broad types:
Sealed - players get a starter deck and some packs to open, then build the best decks that can and play against one another. Usually these happen in 4 series, with the first 3 giving starter decks and packs and the 4th giving extra packs.
Draft - similar to sealed with more player impact. Players pick cards ~70 cards from simulated "packs" that, along with a semi-random base of ~30 cards, form the card pool players. Only one serie in this league.
Constructed - Competitive version of casual play, all cards are available. These can be any number of series and can have all sorts of fun modifiers. The main ones right now are no rares (Poorman's), 1 copy per title instead of 4 (Highlander), and a league to progress through the release schedule (e.g., a serie is 1-7, then 1-8, 1-9, and finally 1-10 aka Movie Block).
Some discussion pops up from time to time in the Valinor board (e.g.,
https://lotrtcgwiki.com/forums/index.php?topic=11463.0) but on the whole comments are simply made in Gemp's chat since there's no need for anything more structured.
Tournaments are automatically set up by Gemp. There are two kinds, daily and on-demand. Daily tournaments happen twice a day at 0:30 and 19:30 server time, and the queue opens up an hour beforehand. If there are 4 or more players in the queue then the tournament starts, otherwise it doesn't. This tournament is Swiss, so players with the same win rates are matched together when possible and everyone plays 3 rounds (with an odd number of players, one person gets a "bye" -- a free win -- instead of playing a match). On demand tournaments are always open and simply fire off once the 4th player joins. These are single-elimination tournaments, lose and you're done. Unlike leagues, you can't change a deck in between tournament matches.
That about covers it, I guess! There's more details on sealed league contents (
https://lotrtcgwiki.com/forums/index.php?topic=9119.0) and the draft (
https://lotrtcgwiki.com/forums/index.php?topic=11616.0) on the forums as well, if necessary.