I will not judge what other people "should have" and "should not have" done. My first buck that wasn't a spike was a spindly 6 that I should have let walk; of course, at the time, I didn't know anything about the way management works.
Based on the picture.. well... lets see
You said he was old, this by no means looks like a yearling. The things I don't know (that maybe you do) are the condition of the teeth. Teeth aging is a reasonably reliable, not to mention cool in a CSI kind of way, process. There are plenty of web articles about it, as well as books. I'm guessing you don't happen to have that particular deer's jaw sitting around, so I'll have to look at the picture.
His face looks kind of narrow, though that may just be angle working against me. The neck, however, looks nice and paunchy, a good indicator of good age and good diet. Again, the angle could be making this assessment totally off.
His body looks a bit wider and larger in mass than the typical yearling. I think just based on the photo, I can't judge weight. Was this deer heavier than most deer you've killed in the same area? Comparing the deer on the hoof, was this deer larger in body mass than the young deer with the bigger antlers? I don't know for sure, based on a photograph. Given the context you've provided, I'd say its likely that this is a cull, however, there is a possibility that this was an underdeveloped 2.5 year old. I can't tell any more from the picture. The difficulty with cull bucks is figuring out what are the characteristics of culls for your area.
I would not regret shooting that buck. I would keep in mind in the future, to carefully assess (not always an easy thing when you see horns, its cold, and you have a gun) the target, and think, "Does this look like an older deer with little antlers, or is this a youngster?".
This may sound selfish, but if you're hunting on land where no one else is following good management protocol, your passing on the little bucks won't matter much, and neither will your taking him.
The best antler restrictions are not legal ones, but ones that emerge from a mutual desire to have bigger deer to shoot, and equal willingness to curb one's own desires and delay satisfaction for the better of the population of deer, so that all might have a CHANCE to shoot really good deer. This is, needless to say, easier on private land owned and hunted on by a few people who are in a partnership that is conducive to good management decisions. This is harder on public land.

I hope this has helped. I can't say with certainty that he is a cull, nor can I say that he looks killed before his time. Maybe some additional information about the deer in the particular area will shed some light.

Sealgair243