I looked at your images and unfortunately it can be both. deer can get an injury while in velvet and they will somehow remeber that injury kind of like a scar. the next year they can grow a new set of antlers and retain that same injury without having to be injured. Now on the flip side of that coin you can have genetics that can do the same thing. If you have deer that have great big racks on your place its likely if you let them live your going to see other deer with great big racks on your place for years to come. However if in your case they have the left anter missing and no injury has taken place your likely to see more deer with a left antler missing.
Speculation: The only way that I think you can know for sure is to capture one of these deer and breed them to see what the results are. However capturing wildlife in most states is illegal and I wouldn’t suggest that.
I harvested a nice buck last year that only had the left side of his antlers. I figured something happened to him during velvet and he was an older deer so I took him. I just check my pictures for this year an there stands another one with just the left side yet a couple years younger. Could this be a a genetic anomily or a coincidence or "Old Lefties" ghost?