There couldn't be less of a direct chain of death between you and the animal. If you don't order that steak its still in the inventory of the restaurant. If you don't buy it at the store its still at the store. If demand actually drops like a stone, I wouldn't be surprised if cows were still killed hand over fist and their bodies turned into mere fertilizer, because a well developed industry is not just going to willingly cease to exist overnight. Once the industry exists and is politically entrenched consumer action can do little to remove it. Take corn for example. We produce so much corn that a huge portion of the crop is converted to ethanol for lack of a better use, and farmers still grow this corn knowing its not going to do much good or feeding that many people, because the industry is entrenched and protected by strong subsidies and costs are high to convert to some unknown industry. We produce so much milk that rather than scale back production when we overproduce for demand, we just dump it into the drain.

If you want to enact the change you expect to enact by going vegetarian, then move to a district with a slaughterhouse and show up to local government meetings every day to raise hell until such land use is made illegal in this jurisdiction. If you rely on consumer demand alone, industry will just find either nonconsumer demand or will use its ability to strongly influence government to keep it in existence in perpetuity.