One thing that SWTOR has that is different and yet works pretty well is a PVP game mode called Hutt Ball. Basically, two teams fight over a ball that they pass around to score goals with. Last I looked, there were two maps. One was a rectangle like your basic football/soccer field(except with a second tier of ramps, walkways, and fire traps), and another map was vertical where the ball would appear on the lowest floor and the goals were on the highest floor.

Since FFXIV has differentiated PVP and PVE abilities, you could do something similar and make each class unique. Star Wars basically has their whole PVE ability set for use in PVP and they have even more PVE abilities than this game does. But the way the mode is played, some abilities weren't used much and some were used a lot more and to greater effect/importance than other modes. Mobility moves and CC/interrupts etc were huge in Hutt Ball.

I don't want to say "blitzball" right away because I'm not sure it would adapt to FFXIV well as is. So if they did it, I think it should be a unique Eorzean ball game for sure, with the first map being in Ul Dah at the stadium.