You don't have to plug the DVD recorder to your XBox. Just plug
the Red-White-Yellow (I don't know the techinical term for it)
wires into the TV output socket and plug the other end as
accordingly to the DVD recorder's input socket. Your DVD recorder
would then be able to record whatever that is showing on your TV
screen.
But of course, if you want to operate the DVD recorder normally,
another bunch of Red-White-Yellow wires are needed to be plugged
into the output socket of the recorder into the input socket of
your TV.
So in total there would be two groups of wires running to and from
the TV and the recorder.