component -> VGA adapters are usually only for Displays where they were too cheap to put normal component inputs so they dual purpose the VGA port to handle both... it's not actually converting it to VGA just using specified pins for component video
if you were to plug that adapter on a normal VGA monitor it would not work.
My old DLP projector (as most older projectors) works the same way.
With that said all you need to hook it up to your 360 is a set of Female to female RCA adapters also known as "barrel plugs" because they're shaped like a little barrel (I think they look more like a log personally
)
I would NOT recommend the use of an Xbox 360 VGA cable with that TV because the Xbox will output a signal in a 4:3 aspect ratio so everything you play or view will look like a "full screen" picture that has been stretched out to "widescreen"
you're better off getting the barrel plugs and setting your output t 720p