I already beat Binding of Isaac quite a lot of times and am trying to max out Samson. Unfortunately, after beating satan five times with that character I still get endgame video instead of entry to the chest. What character-specific requirements are there for the chest?
It sounds like you might be confusing the end levels. As per the wiki, you can access the chest in one of three ways:
Touching the large chest that drops after beating Isaac in the Cathedral while holding the Polaroid. (This is the normal method of accessing the chest.) The Polaroid is a guaranteed drop from Mom if you've beaten Isaac 5 times.
Somehow teleporting to the I AM ERROR room while on the Cathedral.
Finding a Black Market in the Cathedral.
If you've beaten Satan, then you're actually in Sheol, which is the "evil" equivalent of the Cathedral. Touching the chest in Sheol while holding the Negative (the "evil" equivalent of the Polaroid, which unlocks after beating Satan 5 times) will teleport you to the Dark Room.
If you mix these up at all (for example, taking the Negative to the Cathedral or the Polaroid to Sheol), you will not be able to progress to the next floor and the game will end when you beat Isaac/Satan.