If we could limit guns the way the UK has, yes, that would certainly greatly reduce gun deaths.
However, as Beefy said, we have too many guns to go that route.
So, as anti-party said, we need educated gun owners who know how to store guns safely, who don't pull them out to shoot a puppy, who don't leave them loaded near kids.
BUT - since many Americans seem to be morons - we can use laws and technology to help. Trigger locks would keep kids from shooting guns accidentally. Limiting the number of rounds in a magazine and not allowing detachable magazines would limit the number of people shot. FULL BACKGROUND CHECKS - at gun shows, on the internet, when buying from someone who isn't a dealer - would help. What California is doing - if someone commits an offense that makes them ineligible to own guns, California is going to get those guns from them - would help. Limiting number of guns purchased per month across the country, so that someone doesn't buy a lot of guns in one state and ship them to another to sell on the streets.
To also help with the stupidity may require "REAL" gun training classes; not just pro forma ones, but serious classes that people take before they can get a gun. They should also be able to prove they can get somewhere near a target in their shooting accuracy. And yes, we should subsidize the fees for low income people. And then an educational publicity campaign, to tell people how to handle guns safely and to discourage people from even getting them.
And to help with the aftermath - a fee on every gun purchased that goes to a medical fund to pay for the people who are shot by guns.
Would any of this have stopped the guy in the op? hard to say. If we had a culture that frowned upon guns the way we frown upon cigarettes and driving while drunk maybe he wouldn't have pulled out his gun around kids. Advertising worked with those; we need to do the same for guns.
Now I'll sit back and wait for the predictable accusations of being a fascist or whatever.