A couple of decades ago, when I was a member of a novus ordo parish, it was a fact that our priest would simply take Monday off altogether. Presumably, after his Sunday duties were finished, he was "done" till Tuesday. In place of the Monday Mass, there was a so-called Communion Service, conducted by a layperson, usually a man, but sometimes a woman. This priest was no friend of traditional Catholicism and Marian devotion, which he seemed to more or less tolerate with the Rosary allowed to be said by the congregation before only one weekday Mass per week.

This priest has been dead for more than a few years now, and I still pray for his soul from time to time. One of the more unfortunate and sad aspects of my memories of him was that he was ordained in the ancient Rite in the 1950s, yet chose to embrace the novus ordo and the mindset which goes with it. Many of these old priests are dead now or are dying off. We should pray that they will return to the Mass and the Faith of their priestly ordination.

A couple of decades ago, when I was a member of a novus ordo parish, it was a fact that our priest would simply take Monday off altogether. Presumably, after his Sunday duties were finished, he was "done" till Tuesday. In place of the Monday Mass, there was a so-called Communion Service, conducted by a layperson, usually a man, but sometimes a woman.

That situation sounds significantly different from the one described in the OP.  In that situation, it sounds as though the priest says Mass on his "day off," and simply refrains from administrative duties on that day.
Assuming that to be the case, it sounds perfectly reasonable to me.  A priest cannot take a "day off" from his true priestly duties (saying the Divine Office, offering Mass, dispensing the Sacraments, offering spiritual counsel, etc.) anymore than a married person can take a "day off" from being a spouse or parent.  However, taking a day to refrain from the administrative burdens of running a parish and perhaps parochial school is certainly justified.

I know in the SSPX Fr Leath used to take Mondays off in that he would stay in Springfield and go fishing in the afternoon, and drive back in the evening.  Saw nothing wrong with that.  (I accompanied him a few times.)  Of course, he still said Mass and Office- no days off from that.

Our Lady of Fatima, Pray for us, you are our only hope.

"We get a vacation on the day that the Devil decides to take one." - Fr. Zigrang

I wonder which day of the week St. Jean Vianney took.

I have no problem with a priest taking a day off from most of his duties, as long as he prays his office and responds to sick calls when in need. It must be very stressful being a priest and most people need some time off and priests don't get Sundays off.

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There's nothing wrong with giving the priest a day off from administrative duties.  After all, priests are human.  They need a day off from earthly duties like everyone else.  I am a bit surprised a priest in a novus ordo parish has administrative duties.  Isn't there usually an office administrator?  A priest cannot take a day off from his priestly duties anymore than a mother or father can take a day off from being a parent.  

There may be an office administrator but the priest is still in charge.