"the IRS recently recharacterized the RMD as periodic."
I don't think that the IRS has done that (or can even do that at all without a law that changes the tax code). The IRS still might be requiring the payer to take instructions from a Form W-4P, but it's not because RMDs are necessarily periodic payments.
Periodic payments are defined in section 3405(e)(2) of the tax code:
(2)Periodic payment
The term “periodic payment” means a designated distribution which is an annuity or similar periodic payment.
This means that periodic payments are those distributions received as an annuity or a defined benefit plan that is in payout status. It says nothing about RMDs.
For distributions from retirement accounts that are not annuities or defined benefit plans in the payout phase, RMDs are simply a minimum amount required to be distributed. The individual can take these distributions at any time during the year and can take more than the required minimum, so these are not periodic payments even if the payer has been requested to make distributions on a regular basis.
