For non-PVE modes
As a reminder, only games in any matchmaking mode should count. This means any custom games in the game browser DO NOT apply to earning rewards for the weekly challenges. If I remember right for Deathmatch, you must win the top place (not just top 4) to get the bonus point toward the 27 points to unlock the weekly challenge skin. Also you must play the game to the point to where the match is declared in order to earn the points, and leaving any time before will result in not earning any points. I believe there are some rules for backfilling too, but I am not entirely certain.
Remember you earn 1 point for playing an eligible game and 1 additional point for winning that game.
For PVE modes
There is a known bug that Blizzard has acknowledged in the Bug Report forum. Work around this by playing PVP modes instead.