When players want to play Dota 2, they have to rely on several factors to do well. The first is finding good teammates, which is rare enough, and the second is hoping that Valve doesn’t experience any server issues, which can cause errors like “connected to the Dota 2 game coordinator logging in.”
Connected to the Dota 2 game coordinator; login …
Errors like "connected to the Dota 2 game coordinator logging in" often appear when Steam and Dota 2 are experiencing server outages, and this error also prevents you from accessing the matchmaking system. Coordinator stands for Dota 2's servers, and the word appears in other error text.
I have personally seen this error appear in multiple different scenarios. For example, I would receive an error message from the coordinator after I had just finished a Dota 2 match, or shortly after launching the game for the first time. While this error can appear at any time, the impact is always the same and you will not be able to queue for a new match while the coordinator is down.
You can only fix the 'connected to Dota 2 game coordinator logging in' error if the root cause is your home connection. If the error occurs because Valve's servers are down, then waiting is your only option, as a fix from Valve is needed.