Yes.
Yes -- the regulation cited, which says the device must be "approved", and "booster-type seats" are specifically "not approved".
The regulation cited says that (paraphrasing) every occupant of an aircraft has to have his own seat and wear his seatbelt.
One of the
exceptions to this requirement is for a child occupying an "approved child restraint system." The specific provision you cite is a qualification on this exception. IOW, If you are complying with the requirement by putting each occupant in his own approved seat with safety belt, the exception (and the qualification on the exception) are irrelevant.
The exception is necessary for "car seats" i.e, "approved child restraint systems," because when a kid is in a car seat, he doesn't use the built-in safety belt, rather, he's secured by the car seat's restraints. But a belt-positioning booster seat is not restraining and when using one, the built-in seatbelt is used. IMO, the kid in a booster seat is complying with 91.107(a)(3), so the exception shouldn't matter.
I also don't see any difference, regulation wise, between a booster seat and the portable cushions you posted.
I note that the analogous section under Part 121 includes the following
prohibition:
14 C.F.R. § 121.311 Seats, safety belts, and shoulder harnesses.
. . .
(c) Except as provided in paragraph (c)(3) of this section, the following prohibitions apply to certificate holders:
(1) Except as provided in § 121.311(b)(2)(ii)(C)(3) and § 121.311(b)(2)(ii)(C)(4), no certificate holder may permit a child, in an aircraft, to occupy a booster-type child restraint system, a vest-type child restraint system, a harness-type child restraint system, or a lap held child restraint system during take off, landing, and movement on the surface.
The fact that the FAA felt the need to include an express prohibition under part 121, but did not include it under part 91, further suggests to me that booster seats are not prohibited in part 91 operations.
That's just my interpretation; the FAA might have a different one; entertainment purposes only; if you need legal advice, consult an attorney; etc., etc.