I do find the wording of the image a bit jerkish and there's no way anyone in that department would know information that could justify it, but I do have a bit of a situation that comes to mind.
Most people aren't going to dump their original Crystal carts onto their computer. They'll likely be getting the game code. . .elsewhere. The mod will in the vast majority of cases be used alongside this, even though it doesn't -have- to be. Now let's say Nintendo saw the Virtual Console sales of Pokemon RBY, liked what they saw, maybe has a few plans for what else they could put on the Eshop. . .In theory, the ROM hack might encourage the use of piracy instead of purchasing a product from Nintendo. The profit deprived would leave the company with slightly less assets, and thus serve as a slight contribution to Nintendo being unable to have the funds to create more games and products, and people pirating instead of purchasing the game would undercut the work of the original game slightly.
There's times when takedowns are a bit baffling, but just because something doesn't "kill" sales doesn't mean it doesn't have any hypothetical possibility of effecting them at all, and I can see why they might pursue some of the things people are freaking out about them pursuing. When something encourages obtaining an illegal copy of a game or is essentially the same game they are currently selling but better, it's not too hard to understand why they would be uncomfortable with that.
If someone makes copies of your stuff and gives it out for free, it may not be as evil as them selling it, but it still leaves the open door of people just getting the free ones instead of buying from you. It's like asking "Why are you upset I'm handing out for free the same thing you're selling? I'm doing a favor for you!"
I've seen people openly taunting Nintendo on Twitter about their pirating Nintendo's games instead of buying from them. Nintendo is pretty deeply misguided in not going after piracy promoting websites as well when if they care this much about the situation they really should be, but it's easy to see why they might be a little. . .unhappy.
Now, that said, a fangame ruining their image is pretty bull, and there's some fangames that I really can't see any reason why they touched them, but the rest of the points do have hypothetical justifications if you squint a bit, especially since I think I heard someone mention somewhere that they used Virtual Console to pay for their internet servers during the Wii era. I don't think a copyright holder should take down someone's fan works for the most part, but I feel some -not all, just some- of the fan works people have been upset at the takedown of. . .toed a bit of an uncomfortable line between fan support and piracy.
. . .
. . .*puts up flameshield that will probably be largely useless considering how unfortunately heated the topic of copyright gets*