Better analogy: Science tries to understand the game and where it comes from. Religion claims that some guy talked to the game developer, and therefore we all have to obey everything he says.
Not really - empirical science makes the assumption that nothing exists outside of the game (or at least anything that exists outside the game has to be proved from elements within the game)
Empirical science makes no assumptions like that. Empirical science cannot say anything meaningful about things which does not affect reality in some way, however indirectly.
Then in some way, we are in agreement. Science cannot say anything meaningful about things that don’t affect reality. Religion (or theology) concerns itself with the reason that reality exists.
The purview of science is limited to phenomena that can be observed or experienced. The purview of religion (specifically theology) is that which cannot be explained by science (now or ever)
> Religion (or theology) concerns itself with the reason that reality exists.
All religions have a creation myth, but religion cannot be reduced to just the creation myth. That would just be deism which is basically a form of atheism. Religions believe that supernatural forces actually affect the world.