"Thousand-yard stare" is a well-known phrase that stemmed from combat fatigue/PTSD effects on soldiers. It's the distant look (like they're looking at something a thousand yards away) that can be observed on soldiers who've seen some shit. It's almost certainly been picked exactly because it's related to war, weaponry, and the effects of long periods of combat. In modern usage, it's not limited to soldiers -- and in fact, it can be used to describe any distant look from someone who has put up with just about as much of (whatever) as they can stand; it [i]started[/i] as a descriptor of a particular look seen in combat veterans. However, I think it's as fitting as other names for weapons in this game, and not entirely inappropriate. Bungie did similar things with other weapons: "No Land Beyond" comes from a quote centered around the battle for Stalingrad, one of the most intense and brutal battles in World War II, for instance. Fabian Strategy is the name for a strategy of skirmish and attrition, wearing down the enemy instead of having big pitched battles.

I doubt Bungie would make a name for a gun that would offend veterans with PTSD.

I can't speak to whether it offends anyone with PTSD - that is up to the individual person. But I can say with 99.9% certainty that the name was picked because "thousand yard stare" is a) a well-known phrase with connotations of combat and battle-weary soldiers and war, and b) it's a sniper rifle so the name works on a couple levels.