It can be quite annoying to always have those huge games in the list where I dropped out and I am still getting the "unread chat message" message, when it really doesn't concern me anymore.

One thing you can try is to set your My Games filter to "Active games where I am not eliminated." You can set this as your default, and you won't see those games on your list at all anymore.

Sometimes when I am eliminated in a tournament game, the game still concerns me. Even eliminated players can give valuable suggestions to their team. This is why, I feel there is a provision in warlight for receiving messages even when eliminated.

I love giving advice when I'm eliminated. Mostly I get eliminated because I sacrificed myself to delay multiple enemies or larger troops from expanding quickly.
This grants my allies enough time to expand quicker then my enemies and it's always nice to see their superior income per turn lead to a turnaround.
Since I'm a relatively good player (maybe one of the top 100 players here) my advice can sometimes help in making the right decisions to drag a victory out of it.

aranka, it's better to survive, i extremely rarely get eliminated because the extra 5 income is usually more important than the small delay

I don't think this really belongs in the help forum (then again, I don't think this whole topic ever did) but on a related note, I would like to mention how both games in which your whole team is eliminated and games in which you were removed from the game before it began pop back up to the top of your games list each time a new turn is played.

When these are fog games, you can't even see anything about this new turn. However, even when they aren't fog games, most people won't be interested in this game until it ends anyway, at which point it is removed from your list unless it had chat messages (assuming "Active or unread" filter).

adding to this, can there be a setting where its games where it is my turn or have unread chat messages where im not eliminated?