The rules you cite are for US citizens working in the US for a foreign organization or government located in the US, as an employee. For example, employees of foreign embassies in Washington, or the World Bank located in Washington. Those employees receive a W-2 for their wages but no social security or medicare is collected from their paychecks.
That situation does not apply to you because the client for whom you work is not located here in the US and it does not sound like you receive a W-2 from them
