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It can be anyone.

It is an entity that creates zk proofs for the execution of that vProg according to its committed source code, and the de facto transactions addressed to it as sequenced by L1.

In practice, this could be large for profit large entities hoping to make a buck, the "owner" of a vProg in the case of some centralized service, or the users themselves proving their own transactions (not trivial, but within the realm of possibility)


 > The GasPayments map in a Transaction represents the user’s payment for this L2 resource, which is ultimately to be claimed by the vProg’s prover

I'm actually a bit surprised by this sentence, since generally we tried to be somewhat ambivalent regarding inner vProg mechanics, as there could be some degree of freedom and divergence. But I guess it slipped by. 

Anyway point is that regardless of identity of the prover, it is generally a good idea to have a clear monetary incentive to supply proofs.
Generally it is understood that like in Ethereum gas, payment should be in proportion to the work they did (which in this case is overwhelmingly the proving effort rather than execution). This payment is usually assumed to be charged within the vProg itself, as discussed still in the context of based rollups in this post:

https://research.kas.pa/t/fees-and-throughput-regulation-dynamics/247