Decks aren't normally built with slope. They tend to be self-draining due to the board gap, so slope just isn't necessary. You especially don't want slope with decking that isn't substantially textured.
Then, gap is a matter of prerogative. It is often selected based on a number of factors such as local tree debris size and type, appearance preference, and insect mitigation needs.
So that leaves two things in dealing with your problem... gap (or lack thereof) and water retention due to the mat and other objects. Here are some thoughts on all that.
Gap won't entirely eliminate your beading problem. (I don't think of that as "pooling" because it's on a small scale.) However, it could help to a small extent and could help the mat dry out.
Gaps can be added by either cutting slots or holes, or by resetting the decking. Which is suitable is up to you. If you'd like help with that I suggest posting another detailed question.
Consider a different type of mat, or relocate to somewhere that gets light and more airflow. At the stairs or other access points might be better that at the entry door.