Idea for Teeworlds competitive community

Sure. To help explain how ESEA works, take a look at this image from the Wiki page you posted:

ESEA owns a bunch of dedicated servers in different cities. The servers are all dedicated to 5v5 games. You see 11/11 in some servers because there is a "SourceTV," which takes up a server slot. SourceTV is a computer spectator that records the game. At the end of pugs, the demo is uploaded to ESEA.

The ESEA client lists servers in a standard way: map, players, ping, location, etc. You also have a friends list on the side where you can see if people you know are in a game or logged onto the client. The client also includes an anticheat, since hacking is a pretty big problem in CS:S.

You join a server and when ten are in and "readied up": each player types .ready and the server won't start the match until all 10 are ready. If someone doesn't ready up within two minutes, they're booted from the server).

ESEA also tracks stats. So, for example, it will track your AK47 accuracy, M4 accuracy, deagle accuracy, etc., along with other stats like average damage per round and RWS (round win shares; a performance measure constructed by ESEA).

Competitive CTF is played in:
- 4v4 on ctf2
- 3v3 on ctf3

Source

It's really nice that you come up with that effort, but I'm not sure if there is a lot of potential for it to work.
A matchmaking client would take a lot to be made and the motivation is to be found for such an uninterested community.

Maybe if you had come with it 1 year ago, I would have been enthusiastic about that.

In case there's any confusion, the goal isn't to start a league per se. That could come of something like this at some point (going back to the example with ESEA and CS:S, ESEA didn't support leagues for years; now they're the most active league in CS:S), but I don't think it should be the focus as of now. A matchmaking client that pairs players with other players to do pick-up games in a competitive format would make it easy for the average player to play the game at least quasi-competitively. I think the difficulty in designing a client to support this might be overstated. Acquiring enough dedicated servers (I'd imagine ten would be sufficient as a start) will probably a barrier to start something like this, but that could probably be handled without too much pain. Beyond that, the matchmaking bit seems relatively straightforward. Most of the energy spent designing the ESEA client arises from the nature of CS:S. All weapons are hitscan, so cheating becomes a big problem. As far as I can tell, you don't really have this problem in vanilla.

My friend helped designed a few clients for other games. I'll run the idea by him and try to get a sense of how difficult it would be to design such a thing.