There's a lot of differences in the app now. It opts to use a "tip creator" button instead of of showing that dialog. Part of the reason is that the app must implement that flow outside the website, so the simplest approach was taken. We might add this add this in the future, but it's lower priority since the app accounts for a relatively small % of total downloads.
What leaf said - I'd like to add that the small % is about 7-10% these days, and that for the app we can do something much more interesting than ask users to donate before they've played the game. With the app we can ask that after they've played the game for a while, or when they're about to uninstall it, or when they rate it (after they've played it) - there's many options here, and we can set thresholds before prompting the user.
It's not entirely clear to me how to make that non-obnoxious though, I don't want folks to be turned off by the app. So I wouldn't want it to be modal, but that would make it easy to miss. Open questions!
Asking to tip after the user had played the game is a great idea, and I think it would generate a lot of tips for low priced or pay-what-you-want games. Maybe there could be a small inline "Tip the creator" button, under the thumbnail, beside the "Launch" button...? That would be quite discreet.
I don't know about limiting it to the app, though. Why not do the same thing on the "Purchases" page of the site.
Or... notifications. 24 hours after a download, players could get a notification prompting them to rate and/or tip. The notifications could be disabled in preferences.