Good idea.Who says you need to develop linear what is played linear. Movies are not shot linear either.
But you need to be careful with puzzle concepts. If you need to know what you learned in chamber 1 lvl 2 to solve chamber 2 lvl 1, ok. But if you need to have knowledge of chamber 2 lvl 1 to solve chamber 1 lvl 2, that would not be so good.
Same if you would get special abilities from defeating bosses. Or make fun stuff by referencing stuff that did not happen, but you implemented already.