One thing is certain all DNA programmable machines may count as proteins but not all proteins count as DNA programmable machines.
The question in tile assembly systems is how computation can be done by the crystallization process: you could compare them, not to protein function, but to protein folding. The DNA is not being used just as instructions to a machine: there is nothing in this paper but DNA, and the computational work is done entirely through strands of DNA binding to combinations of complementary sequences on the growing crystals: the "instructions" to the computer here are actually the computer itself.