Civil liability for damages is not the same as criminal culpability for a crime. You aren't being tried twice for a crime, you are being tried once for the crime and once for the damage that got caused by the events that appeared to be a crime, regardless of whether you were guilty of the crime. There can still be damages even if no crime was committed.
Automobile accidents are a good example. Even if you get acquitted of criminal charges for reckless driving or vehicular manslaughter, if you are at fault in the accident, you (or your insurance company) are going to have to pay out for the damages caused by the accident.
So the Goldmans didn't have to prove that OJ murdered his wife, they just had to prove that he was primarily responsible for her death and that they suffered damages as a result.