No, religion doesn't claim to transcend everything we do...it claims to be about something that transcends everything we do. ;-)

The large picture, in other words.

Example: In a game, like chess, you make a lot of moves and a lot of thinking, those are the things you DO when playing chess....but surely the original mind(s) that conceived of and created the game of chess itself, not to mention all the other games and the whole rest of life outside of the game of chess, transcend(s) what you do within the mere limits of any one game, correct?

Our lives are brief and limited, quite petty in relation to the larger existence all around us. That larger existence transcends the events of our lives. Religion is about relating to that larger existence. It may or may not posit a "God". It may simply posit a transcendent reality rather than a personalized, human-like God. It is one way in which people attempt to explain what they can never fully grasp...the infinity of existence itself, and the apparent endlessness of time and space. Philosophy is another way we try to grasp the transcendent. Meditation is another way. The more advanced religions contain a great deal of philosophy AND meditation (or contemplation), and that's what gives them merit...not a bunch of silly little petty cultural rules about what to eat on Friday or how long to wear your hair or how many people you should marry or whether or not you should eat pork or how many times you need to pray in one day or what you shouldn't name a Teddy bear.