SP uses a single universal retainer and conversion kit for all their regs with the exception of the Mk 5.
With the Mk 10, 15, 16, 18, 25 etc, it seals using the o-ring on the bottom of the retainer (visible in the LP picture) On the Mk 3, Mk 2 Mk 200, etc it seats using an o-ring seated in a groove above the last thread on the body of the retainer. The universal retainer kit will include both o-rings, or the one on the yoke retainer can be transferred.
That said, the retainer pictured on the LP site is missing the little ridge added to prevent the retainer from being over torqued and bottoming out in a Mk 20 or Mk 25 (added during the late Mk 20 production and retrofitted to all Mk 20's after the recall.) It may just be an old picture, or LP may have gotten their non authorized dealer hands on obsolete parts.
The current retainer is pictured below with the and without the o-ring needed for a Mk 2.
If it is indeed an old part, it would work in a Mk 20 or Mk 25 but with the potential to be over torqued and damage the reg. If that is the case, an SP dealer would replace such a retainer if it came in on a Mk 20 free of charge under the recall.
I am not sure if the fitting being sold by LP would work in a Mk 2 or not - depending on whether it is the current retainer or a really old part that predated the universal retainer. That is the downside of buying SP stuff on-line, it comes by definition from grey market sources and you can never really be sure what you are going to get. The conversion kit runs about $60-$65 at most Sp dealers so for the extra $10-$15 (minus shipping) you are much better off going with a dealer who will also install it and properly torque it free of charge.