There's been a lot of talk here about trademark infrigement -
I want to point out the trademark for Dominion in the goods of computer game software, video game software and online entertainment services is held by Riot Games (publishers of League of Legends: Dominion). Sony previously held a similar mark, but it was abandoned in 2009.
Furthermore I haven't seen any evidence that Rio Grande holds a trademark on the word Dominion in any good.
It's been ages since the one IP class I took in law school, but, IIRC, you are talking about a registered trademark, not a common law or state law trademark. A registered trademark provides certain additional protections/remedies in the event of infringement. One can still have a trademark without it being a registered trademark.
But, setting that aside, the heart of trademark claim/law is the prohibition on selling goods under a mark used by someone else in commerce. The hair splitting as to the industry comes into play later, and usually involves two independently created marks. Further, even if the name "Dominion" is not protected as a trademark, the logo itself and the combination of the same font type/design elements/etc. as are used by RGG in selling their Dominion product likely are. The RGG logo itself is almost certainly a registered trademark, and that is used in this app as well, and further reinforces the idea that this is the actual RGG Dominion app, not a third party fan effort. When, as is the case here, one company is selling (or, in this case, making revenue off ads through offering for free) the same product as is sold by another company, under the same name, and using the same fonts/art/design/etc., that's the heart of a trademark infringement claim - and not one that I'd want to defend.
I don't mean to look a gift horse in the mouth - I like the program (insofar as it addresses my need for a Dominion fix against an AI player), and appreciate that it's a fan effort. But it's so clearly in violation of IP rights that the person who released it should not have done so. I doubt Donald would be any happier with a re-skinned version that still used the same mechanics (particularly given that such a program does exist and such unhappiness has been expressed), but this product incorporates so much of the art and visual style of Dominon that it invites confusion.
Further, I'm forgiving of the program's bugs and flaws because I'm a dominion addict and want to play casually against AI opponents (even really bad ones). I wouldn't be surprised if someone downloaded this program, thought it was rubbish, and incorrectly assumed it was the official version. When the official version is released, that person might not realize that they played an unofficial, unpolished, amateur product (albeit, a good amateur product) and assume that they've already played the game and disliked it.
Again, I appreciate the hard work that went into this app, I'm happy that it exists (at least till the official app is relased - assuming it is better), but I think the person who put it up is being willfully blind of how egregiously their app plays on the official Dominion IP and art.