Yes. The nitrite changes hemoglobin, the molecule that picks up oxygen at the lungs and carries it throughout the body, to methemoglobin via a reversible oxidation reaction. The heme iron is oxidized forming ferric iron, which cannot bind to oxygen. The body has a process which reverses this reaction but the sheer amount of nitrite totally overwhelms that system and it cannot reverse this oxidation quickly enough to keep your levels of methemoglobin low. When you have a high percentage of methemoglobin, that means a high percentage of your blood cells can't even bind to oxygen. Without oxygen our tissues die. So this is a death by hypoxia, as stated in many places.
Edit: If I got anything wrong, feel free to correct me I am not omniscient and will not be offended