You can read servers being congested in two manners
  1. First: More technical, network/server congestion, when you're talking about an issue/problem
  2. Second: The literal, and most known, direct English meaning of the word: full

Now if you're around engineers and are having network issues, you'll probably be using the term congestion.

If you're a business running a service for a bunch of users with no technical knowledge, I doubt you'll be using technical slang, thus I believe the use of the word "congested" goes as a synonym of "full", without need of it to being related to network issues; which I suppose is what they're doing.

Honestly, even if their servers suck, I don't see a company going "HEY OUR SERVERS ARE SO LAGGY RIGHT NOW YOU BETTER STAY AT THE DOOR", not the best marketing approach.

Googling "server congestion" and clicking on the first link (Network congestion) can mislead you to confuse technical slang with a more plain meaning of the word: "The servers are full."

Now, if they don't let you login because the servers are full, they're doing this because if they allowed more people, the servers would be way over their capabilities and then real network congestion issues would start (such as lagspikes).