Score used to be important in video games. With the rise of Guitar Hero and the Xbox Live Achievement system, it's coming back, but it went out of style for a long time. High scores made a lot of sense in the arcade (which has also gone out of style) since other people played the machines and could thus compete to overtake your three-letter tag as that machine's leader. Home games adopted scoring for two reasons: first, in the older games, there was no other way to determine progression. After twenty minutes of Asteroids, without a score there'd be no evidence that you'd done any better than someone playing for thirty seconds. The game never changes, never reveals new content, and never ends. Score was a very simple way to allow you to progress. Of course, competitive sport-based games like Pong required scoring as a basic gameplay mechanic.
Later (NES and beyond) games adopted scoring mostly as a holdover from classic arcade games. Games like Super Mario Bros. were more about experience than performance, and progress could be tracked by ... actual progress. You moved from place to place, and didn't need some arbitrary number to tell you how far along you were. Even the first Mega Man game had a score display.
The first Castlevania arguably didn't need a score counter at all. Not dying was more than enough of an achievement to wear as a badge of honor. Besides, it already featured another counter in the game (hearts) that also incremented by picking up items. Later Castlevania games adopted experience points, which are exactly like points except that their accrual actually improves your avatar's abilities, but pre-Symphony of the Night games all awarded points for killing enemies and collecting items.
Some of the items, in fact, did nothing but improve your score.
