I know that Angry Birds is available as an online HTML5 version at http://chrome.angrybirds.com/.
I have an iPad, but I cannot install apps onto it, so I'd like to download the game so I can play it on my iPad (I think the iPad can render HTML5).
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The culprit here is actually your browser -- the device you are using is actually reported to the website by means of your browser's "user agent". The user agent tells the website what device and browser you are using. So, it makes sense that the only way to fool the Angry Birds website is to send a different user agent.
I'm assuming you can't jailbreak your iPad and modify the browser, but there is a method to modify the Safari user string without jailbreaking. However, you do need to be able to sync the iPad with your computer. Here is a link with instructions. Aside from that, you might be able to find a web proxy to change your user agent, but I don't know of any that will do that. Let me know if this helps.