Well, this is part of the terms and conditions for earning points. Unless I reading something wrong, I think you're entitled to the points.
A Member is eligible to receive Points/Miles for staying at participating
Marriott brand hotels or Ritz-Carlton hotels for his/her room and up to two
additional rooms. At least one of the rooms must be reserved and registered in
the Member's name and the Member must pay for all rooms, which payment
arrangement must be requested at time of hotel check-in. The Member must also
stay in one of the rooms. To ensure Points are automatically posted to the
correct Membership Account, the Member's Rewards Program Membership Number must
be present on his/her room folio and up to two additional rooms, as
Except apparently when you buy a Marriott Encore Week for your own personal use - purchased directly from a Marriott Sales Associate while staying at a Marriott property ... Marriott calls that a "wholesale package" but there's nothing in the fine print or Timeshare Sales Presentation that mentions that lack of Elite Night and MR Points credit. Had I known about that lack of credit, I would never have spent the $1,600 or so on an extra week... Not cool, Marriott. You're better than that!
In view of the other replies, I would you suggest booking one of the two sets of stays at the Marriott and the other at another local hotel at which you have elite privileges so that you can get full points.
I recently stayed at two ACCOR hotels in France (for which I was not the named designee nor did I pay anything) and yet because I showed them my ACCOR Platinum card I got credit and points. Go figure.