That's what my nephew said when I asked him why does he not watch YouTube on his iPod.

He watches a lot of YouTube on his Xbox but I always thought iTunes is installed on iPods iPad etc just like Google play/android market is installed on android devises.

Am I wrong?

you don't need itunes to watch youtube on an ipod touch/iphone/ipad.
you simply download the youtube app.

itunes is what you install on a pc/laptop.

So what store is installed on iPads/iPods as surely you must download it from somewhere?

App Store.
it's the blue icon with the white "A" in it.

Do you need to setup an account to use it like email and bank details?

Yes, but you need an iTunes account which you have to activate through iTunes, so yes, he does need iTunes to downlaod apps - even free ones.

However, can't he just use the web version?

He had a bit of a strop and shouted 'I need tunes' and left the room when I asked him as my sister asked him too.

Must be an account issue.

you can set up everything on the device (hence the "post PC era". you can create an itunes store account using a pre-paid gift card if you don't want to use a credit/debit card.
http://support.apple.com/kb/ht2731

however for free apps you don't even need to provide any payment details.
http://support.apple.com/kb/ht2534

he doesn't need the actual itunes application installed on a pc/laptop.