I disagree, it's not particularly useful.
Nodes don't vote just by running. They vote either by relaying a transaction, or by mining.
I don't agree with Mike. Bitcoin is not a democracy— at least not a majority voting one. It's not a system that is predicated on a "vote", it's a system predicated on autonomous validation and it would not be trustworthy if it were predicated on relaying based voting as sibyl attacks would undermine it. The only "voting" in bitcoin is the computational vote on the ordering of transactions, which we don't know how to resolve absent a vote, and a non-mining node doesn't actively participate in that (though they do passively participate in that by forwarding only valid blocks— which is essential but rather indirect).
A non-listening node contributes through the basic services of honestly relaying transactions and blocks, but it also contributes to the security of the system by making sure that any violations of the system rules are ignored as effectively as possible. They do this even when they are not providing listening services so that Mike's SPV clients can externalize their cost of running their own validation... though it is obviously much more valuable when a node provides this service to nodes which lack the validation. The existence of many relaying full nodes, regardless of if they listen, is one of the reasons that the "red balloons" attack (where miners selfishly fail to relay txn with good fees) is not a practical issue and also doesn't depend on the relaying nodes listening. Another way they help is by improving privacy for other nodes by relaying transactions and thus further obscuring their origins.
An extra point to add is that a node especially contributes when it is better maintained than the average node— because it can increase the speed and reliability of transaction and block relaying network wide. E.g. because the average node is on some slow spinning disk, a fast node which stays up with current software, and runs on a SSD or ramdisk can contribute quite a bit. Faster relaying makes forks less likely which makes zero and one confirmation transactions more safe for those foolish enough to use them. A node can also contribute better when it's crossing transports— e.g. talking to nodes on IPv6, and talking on Tor (and maybe listening, as it's possible to listen on tor even for some nodes that don't listen generally) as there are far fewer nodes on the other transports.
