It just has to be designed in such a manner as to not inflict superfluous injury in order to be used against uniformed combatants. The round pictured looks like an M855A1, which certainly fills the requirement.
Back in 1990, the Army Jag Corps approved the use of the M852 7.62x51 match grade boattail hollowpoint for use by Army snipers. The memorandum I linked to explains the rationale in light of the text of the Hague Convention language.
The US was and is under NO obligation to abide by the Hague and Geneva Convention ammunition standards when killing Osama bin Laden. Osama has never been in uniform, he is not a soldier in a nation that is a signatory to any of those agreements, and he is both a common criminal AND a savage. So you can see, any number of exemptions applies to him. It would have been PERFECTLY lawful to use nerve gas on him. I would recommend any firearm ammo suitable for use on soft-skinned big game, like deer.