Absence of one light source does not affect the brightness of another
The brightness of a torch is not contingent on overlapping its light with some background light source, such as moonlight. This is evident from the fact that a torch works just as well underground in a pitch dark cavern (where there is certainly no moonlight) as in a moonlit (or non-moonlit) night on the surface.
Furthermore, moonlight is normally already considered darkness, as spelled out in the description of darkness in the Vision and Light section of the rules (emphasis added):
Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a subterranean vault, or in an area of magical darkness.
So there is generally no mechanical difference between a moonlit night and a moonless night anyway.
I can't find anything in the rules that explicitly spells out how lighting from multiple light sources combines, but the most logical rule I can think of is: the brightest light source prevails. That is, if a object is illuminated by both a bright light and a dim light, that object is brightly lit. If another object is illuminated by two sources of dim light, it is dimly lit.
However, your DM can make new rules
Despite the above, the DM can implement any rules they like. It's possible that the "nonmagical" darkness of this moonless night is just a different kind of magic. The Sage Advice Compendium explains:
You might be thinking, "Dragons seem pretty magical to me." And yes, they are extraordinary! Their description even says they’re magical. But our game makes a distinction between two types of magic:
- the background magic that is part of the D&D multiverse’s physics and the physiology of many D&D creatures
- the concentrated magical energy that is contained in a magic item or channeled to create a spell or other focused magical effect
In D&D, the first type of magic is part of nature. It is no more dispellable than the wind. A monster like a dragon exists because of that magic-enhanced nature. The second type of magic is what the rules are concerned about. When a rule refers to something being magical, it’s referring to that second type.
Given this, it would not be unreasonable for the DM to decide that in the world they are building, the darkness of a night with no moonlight is not a mere absence of light, but in addition it has a slight supernatural edge to it that makes all light a little bit dimmer. This would be especially appropriate in a horror-themed campaign.