Conquer Club

Do you get Conquer Credits from playing/winning games?

Not from your every day games, no. You can earn them from participating in the various community events going on listed at the top of the page or from Autotournaments (Click on Tournaments at the top of your screen - on the right are auto tournaments.. they list the prizes on that screen). Some regular tournaments might offer credit prizes as well but you'd have to explore the thread of each one to figure out which.