As far as I know, noone has ever drowned playing underwater rugby or underwater hockey. Yes, it does take time even for a swimmer to get used to snorkeling and automaticly clear the snorkel coming to the surface, so newbies do swallow water in the beginning, but it's the same as learning to ride the bicycle, a couple occasions practicing and your good to go underwater!
Recurring concerns of outsiders are shallow water blackouts. These faints are caused by ( mostly conscious) hiperventillation, meaning frequent respiration or overbreathing, above 20/minute, aiming to vent carbon-dioxid from the body and increase oxygen concentration, as the intense exercise done underwater uses up the body`s oxygen supplies.
It is important to know that the urge to return to the surface and breath is not caused by the lack of oxygen in the lungs, but the increasing rate of carbon dioxide. So the blackouts are consequences of dangerous techniques meant to push the human limits of apnea further and further, and have nothing to do with swimming or finswimming actually. You could even test it with doing hiperventillation for a minute and then doing squats breathhold, but I would not recommend it.
Besides, unlike in other freediving sports, in underwater games no award is given to those who can stay underwater for a long time, what matters is scoring! And you may do that easier if you manage your time underwater well and spend enough time on the surface not to run out of breath underneath.
Of course people can faint for other reasons too, there is a reason why lifeguards are watching over swimmers or waterpolo players at pools. But trust me, 11 other players and 3 referees would notice right away, if someone would need first aid.
Underwater games carry some risks as well, but the chances of the common sport injuries ( runner's knee, sprained ankle, etc. ) are slim as the drag of the water absorbs the few impacts which occur during the game. In fact, underwater rugby and hockey offer the same benefits as swimming! Building muscle mass, increasing flexibility, improving cardiorespiratory fitness, burning lots of calories and staying healthy. They can be played for a lifetime ( I know great players who are above 60 ). Not to mention the mental aspects. Being a disciplined teamplayer is crucial for success in underwater games as even the top athletes run out of breath at some point and they need to rely on tactics and teamwork just as much as anyone else.
Injury of the leading hand is the most common accident in underwater rugby. That is why we find it important to tell everyone to clench those fists as much as possible… Like always. Yes, we do have scratches from fins and maybe bruises even sometimes, but after all, it is rugby underwater!
The game itself is not violent at all, and there are various penalties described in the rules. Underwater scuba refs make sure these rules are followed at tournaments. Don't worry about being tackled by other players, if you let go of the ball they will let go of you as well. If you are insecure about your swimming skills, again, don't worry. It only takes a couple trainings to get used to finswimming and snorkeling, and you are ready to take take on the world of underwater games.
And a shout-out to swimmers, divers and waterpolo players : give it a try, show us the best you've got!