Bejeweled Blitz

when you say 'new' do you mean the second gen? it's nearly a year old, not sure i'd call it new anymore 😉

is it in the App Store, or is it in the 'Games' section of iTunes? Games in the games section are designed for the older iPods and will not work on the iPod Touch.
if it is in the app store, it will almost certainly work, most apps will work on both the Touch and the iPhone, in fact generally i've found if they only work on an iPhone I won't be able to download it.

Bejeweled Blitz appears to be a game only available on Facebook:

http://en-gb.facebook.com/apps/application.php?id=40343401983

so no, you can't download it to an iPod touch. Online games are often written in Flash which won't work on an iPod touch. I don't use Facebook so can't check.

Easiest way to find out is to just try it yourself.

Bewjeweled 2 is available from the AppStore though:

http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=284832142&mt=8