Now I have no clue why Amazon has this rule on twitch for the iOS app as its a strange rule but yes as long as you check in a browser you can claim. I have gotten the drop page to open in Firefox on iOS and it shows progress just fine even while watching on an iPad. though if you want it to change I would say people should start bugging Twitch, At a minimum maybe they will tell you why such exists.
Safari will usually try and open the app, Chrome will sometimes try and open the app, I have had the most luck with forcing Firefox to request the desktop page. Will be interesting to see if this policy also applies to Android when that version drops.