Defining "white phosphorus" as a chemical weapon is a new one. While technically, white phosporus IS a chemical, so is the smokeless powder used in bullets and the conventional explosives used in bombs, grenades, and the like.

Words have meanings, including terms like "chemcial weapons". From the DoD Dictionary of Military Terms:

chemical weapon

Together or separately, (a) a toxic chemical and its precursors, except when intended for a purpose not prohibited under the Chemical Weapons Convention; (b) a munition or device, specifically designed to cause death or other harm through toxic properties of those chemicals specified in (a), above, which would be released as a result of the employment of such munition or device; (c) any equipment specifically designed for use directly in connection with the employment of munitions or devices specified in (b), above. See also chemical agent; chemical defense; chemical dose; chemical environment; chemical warfare; riot control agent.

From that definition, white phosphorous isn't defined as a chemical weapon. It can kill people, primarily though burning, but the design isn't intended to kill through toxicity. By international definition, chemical weapons include things like mustard gas, nerve gas, blistering agents, and the like. From Global Security.org (emphasis added)

White Phosphorus (WP), known as Willy Pete, is used for signaling, screening, and incendiary purposes. WP is a colorless to yellow wax-like substance with a pungent, garlic-like smell. White phosphorus, a pyrophoric material (ie, spontaneously flammable), creates a smoke screen. A side benefit of white phosphorus is that white phosphorus smoke is toxic and readily penetrates protective mask filters. Phosphorus smokes are generated by a variety of munitions. Some of these munitions such as the MA25 (155-mm round) may, on explosion, distribute particles of incompletely oxidized white phosphorus.

White phosphorus is not banned by any treaty. The United States retains its ability to employ incendiaries to hold high-priority military targets at risk in a manner consistent with the principle of proportionality that governs the use of all weapons under existing law. The use of white phosphorus or fuel air explosives are not prohibited or restricted by Protocol II of the Certain Conventional Weapons Convention (CCWC), the Convention on Prohibitions or Restrictions on the Use of Certain Conventional Weapons which may be Deemed to be Excessively Injurious or to have Indiscriminate Effects.

When I was in the Army, one of the weapons we were trained on was a white phosphoruos grenade. It was about the size of a beer can and was primarily used to start fires and to generate a smoke screen. As I recall (this was 30 years ago), an average soldier could throw one of these grenades about 15 meters but the damned thing had a 20 meter bursting radius. Nasty business. White phosphorous rockets have been used for decades by spotter planes to mark targets, although this is less common since laser and GPS guided bombs entered widespread use. It has also been widely used in artillery shells and mortar rounds, primarily as markers and smoke rounds.