The component to RGB adapter pictured above will only work if either the DVD player massages the video signal first (into RGB) to be compatible with what the projector wants or the projector will accept what the DVD player gives it (component video). Any needed adjustments, if available, are manually done.
A small number of upscale A/V receivers will do the massaging. There are also dongles called transcoders that do. Being able to switch component video does not automatically mean being able to change it to RGB.
(Very vague hypothetical analogy) Imagine the DVD player is putting down the red, green, and blue cables (or HDMI cable) signals for red, white and blue while the projector wants red, green, and blue. You finish the story.
In addition, hi-def DVD players will throw away half the resolution (like HDTV's with cheap 1080i to 1080p conversion) if the recipient (projector) is not connected via a HDCP compliant digital input. For this reason I would not bother with Blue Ray for a run of the mill office projector. Furthermore, if the recipient actually does have cheap 1080i to 1080p conversion, it may throw away up to half of what remains. (You'll still get more than what you got with S-video cabling.)
Video hints:
Component Video