I think it is definitely too dated in appearance. I'm not really a fan of websites which use a colour backgrounds for the main content area. It can often to be too hard on the eye and off-putting.
I think something still quite playful would work, pulling out tones, shapes, styles and colours from the logo. 15 minutes messing around in photoshop gave me this...
It's by no means great itself, but just a visual guide to my suggestion.
I think something still quite playful would work, pulling out tones, shapes, styles and colours from the logo. 15 minutes messing around in photoshop gave me this...

It's by no means great itself, but just a visual guide to my suggestion.