He doesn't; he says not to do so during public worship because of the disruption it caused as it was then managed. His solution was not to bring some order or ceremony to it but to take it outside the service altogether. p. 353.
My OP contacts speculated it is because he is in NH as is the editor and because he is as close to a conservative Presbyterian as you will find in NH, Sabbatarianism being a defining mark of Presbyterian such that Hodge was of the opinion that without it, you ain't one, which makes the guy a better Presbyterian than most.
For what it's worth, Chapter 22, paragraph 8, of the 1689 London Confession is almost identical (minor changes in a few words) to Chapter 21, paragraph 8 of the WCF regarding holy rest, works, worldly employment and recreations, etc. Some of the most convicting modern sermons and writings on the subject come from the Confessional Baptists I associate with.
Well, that's the thing; RB's once they decide to own their confessional heritage, they own it. They don't carve it up like Jefferson's bible as in the PCA, etc.