This is certainly an interesting one. I hadn't read the xkcd comic it's based on, but when I did I howled with laughter and adorableness--that's a great comic to choose for a game. :)
The game itself is pretty fun, but has quite a few flaws. I love the mechanics as described in the "How to Play" screen, but some things are left to see only in play. For example, I thought you had to get pretty close to the buns in order to alert people and be happy, but that made me only startle them, which got me frustrated. It took quite a while to understand that I had to get kinda close, but not too close, in order to record the bun. It would also be great if a specific number was assigned to buns and flashed as you got the happiness; you say small ones are better, but as a player I can't really see the difference. I do love that, though, that small ones are better for your happiness/popularity (and that small ones are called "King Bun"). X)
The run speed is fine, but the animation that goes with it make it seem slow when it's not. I guess it does pair well with the music though, which I have mixed feelings about--on one hand, it's kind of over-the-top cheesy-happy piano, but on the other hand, it's perfect music for a person who lives to give other people alerts on their phone about rabbits, the kind of music that would play as that person gets an existential crisis about what they've done with their life, or when their ignorance consumes them as they happily chase buns for the rest of their days.
I like and hate the idea that there are other bun-searchers in the park with you. On one hand, that means there's competition and drive to succeed. On the other hand, it makes approaching buns really frustrating when someone else startles them away, and another person startles the startled bun, and another person--you get the idea. My biggest issue with this is that, because people startle buns in the middle, pretty much all the buns are found on the edges and walls of the park, making this game about "searching" for buns into "go to the edges and walls and be happy forever".
Though the upside of the multiple people that they can startle a bun right into you, and it will relax as it approaches and give you points. As I write this review, I've kept the game open in another window, and people have been running buns into me every so often and keeping me alive. It's weird and sad to say that my game has been nearly at its best with me just standing still--which I'm sure is not at all what you wanted.
There are a few bugs with the user screen--I've appeared multiple times on it when catching multiple buns. Also buns disappear sometimes if they hop on the wall too much--was that intentional?
The coordinates that tell you where a bun is is a nice touch, but not super helpful since the space is so big. By the time I reach it, the bun's probably gone. It's a good idea, though. Also, the sound design in this game could be much better than it is--perhaps have a sobbing sound when people collapse to the ground? Or a nice sound effect when you get happiness from buns, and a even more awesome one when you get a "king bun"? The sound could really elevate the design here.
Overall, this was a nice game! Great job with it. :) BUN SPOTTED.