There are no external safeties for the operator to engage with these handguns. They will only go off the trigger is pulled - so drops should not set it off, nor the actions in the video. You have to intentionally pull the trigger for the gun to go off, which is the ultimate last word in safeties.
There are still semiautos with external safeties hammers, the most famous being the 1911. These are what's called single actions. The trigger weight (amount of pull on the trigger) is relatively light, so they have an external safety for the operator to engage/disengage.
I personally prefer single actions, hammer cocked, safety engaged, but this is always a very, very personal preference by people that carry. I own Glocks, but I would not carry one because of the lack of external safety, however, I would never criticize anyone that does. This is 100% strictly boils down to what the person is comfortable doing.