By Yevon they can!
After all of them start speaking over each other (except Keepa, who's silent), and then a moment of quiet as they all stare at each other and some background dominance contest takes place, Datto starts explaining.
Blitzball is played in a spherical water stadium (Jassu puts in that the stadium is just literally made of water and they use antigrav tech to make sure all the water behaves as if it were inside a perfectly spherical container) between two teams of six players. Two triangular goals are set in the water on opposite half-spheres of the stadium, and each team takes position in their half. Starting positions aren't fixed by the rules except that the goalkeep has to start in front of their team's goal and there's a minimum distance each player has to be from each other. The teams consist of three fielders, two defenders, and one goalkeep: the fielders' job is to try to navigate past the other team and shoot the blitz ball at the other team's goal, which scores their team a point; the defenders' job is to stop the other team from getting to their goal; and the goalkeep's job is to prevent the blitz ball from successfully entering the goal if all else fails.
At the start of a game the ball is shot up into the water from below, and one fielder from each team has to try to grab it first. Players typically hold the ball under one arm while swimming, which of course makes them swim more slowly so it's not ideal to try to have a single player keep the ball to themself throughout. An opposing team's players can at any point attempt to steal the ball from the person who has it, and while this is not explicitly mentioned it seems from Datto's description that the game gets very physical then, with actual tackles and magical techniques being broadly allowed. Players can also pass the ball to each other, and anyone is allowed to try to intercept a pass.
There isn't an actual distance limit a player has to be from the goal to try to shoot the ball into it, but they do have to take physics and potential interceptions into account. Shooting a ball can be done either by throwing it or by kicking it, and there are also magical techniques to do it, as well as magical techniques to enhance goalkeeps so they can do their job better. Once a team scores a point, both teams reassume their initial positions and the ball is removed from the field to be thrown into it from below again (of course they usually just use multiple balls instead of trying to always recycle the same one, interjects Jassu), but that time only a fielder from the team that suffered the most recent goal is allowed to grab it.
The game lasts 60 minutes total, with two 25-minute-long periods and a 10-minute-long break in between. Teams are allowed to change their starting positions at half-time. It's typically allowed to replace players at any time during the game, but an active period will not be paused for it unless it happens due to incapacitation. At the end of the second period, the team with the most points wins. If they're tied, they go into death match mode, with the first team to score a point taking the victory.