A few insights that might help in this matter.
First, any sport needs an appropriate method of beginning the game. For humans, it may be a rousing rendition of the national anthem. For dwarves, however, there is only one appropriate way to start a round of the Sport of Underkings: bringing a noble up before the crowd to speak, and then dropping him into the magma. When his body disintegrates, the cages open and the game begins.
Second, as with any game of this nature, not all players have the same tasks. You have two Strikers, armed with hammers, whose goal is to launch goblins as far as possible horizontally. Then you have two Choppers, armed with axes, whose goal is to launch goblin chunks vertically onto the scoring platforms. Finally, on each team, you have one Sniper, who will attempt to kill the goblins on the other team's side before they can be launched.
Third, the arena must be properly maintained. The floor is engraved, the pathway up to the stadium should be lined with alternating sculptures and caged beasts, and there will be accommodations for both dining and festive parties (read: a food stockpile, kitchen and brewery, and dining area laid out with a view of the proceedings, along with a large enough dance hall for dwarven raves. Preferably illuminated by a magmafall, one being used to feed the arena cleaning system.), along with (once the economy starts) stores for spectators to buy commemorative memorabilia (read: crafts and clothing shops). And ample seating, preferably in tiers. If possible, use a glass roof to let a bit of sunlight into the place. An infirmary for injured athletes would be nice, but not essential.
Fourth, if possible, make some arrangements for interesting fights. Arrange for the floor to flood with water to allow aquatic fights, throw in exotic enemies, stage ordinary gladiatorial bouts, redirect sieges into the arena, and use kitten disposal as an opportunity to give your athletes some practice. Also, if it is in fact possible for goblins, elves or humans to breed in captivity, arrange for such to ensure a steady supply of replacements for the games.
Last, but not least, make sure to have fun.