Parody!

Newt Scamander: So, let me get this straight…you took my book, a book that I spent most of my teenage years writing…a book catalaguing every Meridinaite creature ever…and you improved on it?
 
Fluttershy: Well, no offense, Mr. scamender, but your book was missoing several Equestian creatures…
 
Newt Scamander: I’m just fascinated to find someone in Equestria who cares about magical creatures as much as I do…
 
Fluttershy: Mr. Scamander…I grew up reading your book. You are my personal role model. And caring for magical beings…it’s my destiny…
 
Newt Scamender: My little pony…I’m 75 years old. I can’t carry my work anymore. My son is married. My grandchilden are teenagers. Meridian doesn’t care for zoologists anymore. I’ll be more than proud for you to carry on with my legacy.

@Pagan  
Given that the griffons are sorta Central Asian, I wonder if the ‘living ball’ is some sort of reference to a game like polo that the Mongols and Afghans play from horseback? Of course that one involves a dead goat. Or at least it’s dead by the end of the game…

There was a series called Galaxy High where they played a sport with a living ball. It was not only alive but wanting to be hit.

Fantastic Beasts and Where to Find Them
 

@dynamicv
 
That’s probably it.

@cheezedoodle  

You might actually be thinking of the somewhat poorly reviewed 2006 Walt Disney animated feature The Wild, which featured a scene in which turtles were used for curling.

@cheezedoodle
 
@Pagan  

@cheezedoodle  
Alice in Wonderland maybe?

I wish I could remember which cartoon it was where a game took place using a live animal as the ball. For some reason a turtle as a hockey puck comes to mind, but even after several google searches I can’t come up with one.

@Background Human  
If we stay with the idea that boffyball is to association soccer as hoofball is to american football, the idea of not flying is equivalent to not using your hands. While that’s not an ejection penalty, that is a huge no-no in the professional sport.
 
That said, they’ve also affirmed this is an “international” sport (Saddle Arabians play) so it likely is a means to make it fair to all species that you can’t fly off the ground, use magic, use hands, etc.

So my initial speculation was right for the wrong reasons, a fluffy critter for a ball. Fluffy (something) abuse is canon.  
Also, this strict flight ban would have been a good rule to establish before that iron pony competition.

Ejected for flying? Seems needlessly harsh. Most sports don’t toss you for a single rule violation unless there’s some serious unsportsmanlike conduct involved.
 
And I’m probably putting far more thought into the rules of boffyball than the writer ever did. What can I say? Fictional sports fascinate me almost as much as real ones.

@DeeperMadness  
Gilda’s plan B

I ship it.
 

 
Rarity’s seen some _yay, yo.

thats animal abuse!

Huh. Usually it’s Twilight who gives the awful, interminable lectures.

The ball is alive? What is this Eldorado?

@PonyPon  
Fosgitt’s style is more suited toward Looney Tunes things. Everything has that Tweety Bird look to it.

This looks really weird.

Also, I don’t know if it’s just his style or what he thinks they look like, but these other griffins remind me of Disney birds.

Okay, so it pretty is that other fantasy sport.
 
Boufball is this sport’s inspiration.