Given the explanation it's not unreasonable to assume the programmer doesn't actually see himself in the wrong, after all the initial agreement was that ADWCTA and Merps come on as consultants with a 80/20 split of the profits, but now when the site begins to get more popular they begin asking for an equity steak in the project rather than just a share in the revenue.

Obviously grinning goat gaming originally didn't think they'd invest so much time into this, they went from consulting to very hands on with the production of the whole thing, advertising it, optimizing the algorithm, explaining how and why things should work a certain way to the programmer.
At the end of the day they weren't just consulting, they were partners in the project, HA wouldn't be where it was today if it wasn't for them.

But from the programmer's perspective, this is just a side project for GGG, after all they're not living off their savings to fund development for the project, they have their own jobs and won't overly be effected by it if this project fails rather than disappointment and a slight reduction in income, but if this fails for him, he's suddenly jobless.

Does that mean he's right?
Well no, GGG have put in at least the effort to make a reasonable argument for some equity in the project, after all the project would have failed long ago without their experience guiding it.

Does that mean GGG is right?
Well, still technically no, it might not exist without them sure, but what if they suddenly decided they were bored of Hearthstone? That it's no longer worth their time and they had more important things to work on, suddenly the programmer is left in the same position if they had just left outright, but is still gimped by the loss in shares from his endeavor.

The decision itself still seems rather shortsighted from the perspective of the programmer though, his work will never become out of date but GGG's work has a timer on it until it starts getting slowly out of balance, plus a lot of the active userbase comes from the content creators driving users into the site rather than simply positive word of mouth from the application. But, maybe he thought of that? Maybe the reason he wanted to give profit shares rather than equity steak isn't because he's selfish but simply as a safeguard, functionally GGG will be getting the same payout from the application, the only difference is if they ever decide to leave the programmer won't be in a bad spot.

If you watch the film "Indie Game: The movie", the developer of Fez was put in a similar position the developer of HA would be in if he gave an equity stake and GGG decided to pull out of the project.