It's the wrong word. It should be 'regimen' ( without the 't'). regimen: a prescribed course of medical treatment, diet, or exercise for the promotion or restoration of health

No answer, just thinking by writing: Although I did not recognize the problem for a moment, the AMBIGUITY seems to be clear: REGIMENT does mean a military formation of people AND is at the same time an obsolete synonym for forcing “discipline or order on, esp. in a domineering manner.” (cf. Collins Dictionary, also Oxford Living Dictionaries.) The meaning of Jason Mey's example sentence is clear: Here "REGIMENT" stands on the one hand for a military formation (in the first part of the last sentence), on the other hand for “REGIME” in the second part of the sentence. Another funny example: “Never underestimate that monstrous regiment of women’, I said.’” (Oxford Dict.) My understanding: No regiment of Amazons fighting against poor men regiments, rather a very strict matriarchal regime. Do you agree?

It means that that the rules at meal time were very strict ( followed a strict system or pattern).