I never read the manuals to metroid or super metroid, and I managed to beat both of them. When I was 10.
Really, even though how to open red doors is in the manual, you don't need the manual. You open -every- door by shooting it, it's one of the few ways you interact with things. So when you first come to a red door, your first instinct is to shoot it. But your normal bullets bounce off of it harmlessly. What's the next logical step? SHOOT IT WITH OTHER STUFF. Everything except for missiles bounces off of it, and when you hit it with a missile, it reacts. That should be your clue to keep shooting it with missiles.
Everything you need to figure it out is in the game.
Somewhat off topic - is there a particular reason that random words or phrases in posts are linking to random ad links? Has this always been going on? I just recently whitelisted all of HF so, just curious.