What I mean is a parody/spoof is a comical adaptation.
The opposite would be a dramatic adaptation.
For examples, both Batman: the Movie (1966, Leslie H. Martinson, Disney/20th Century Studios) and The Dark Knight Trilogy (2005-2012, Christopher Nolan, Warner Bros. Pictures) are Batman adaptations, one has everything played for laughs, and the other has everything played for drama.
I would call that a tragedy because it rhymes with parody.
I do not think that a parody need be comical or humorous.
The Merriam-Webster definition (sense 1) reads:
a literary or musical work in which the style of an author or work is closely imitated for comic effect or in ridicule // wrote a hilarious parody of a popular song
The lead section of the Wikipedia article reads:
A parody, also called a spoof, a send-up, a take-off, a lampoon, a play on (something), or a caricature, is a creative work designed to imitate, comment on, and/or make fun of its subject by means of satiric or ironic imitation. Often its subject is an original work or some aspect of it — theme/content, author, style, etc. But a parody can also be about a real-life person (e.g. a politician), event, or movement (e.g. the French Revolution or 1960s counterculture). Literary scholar Professor Simon Dentith defines parody as "any cultural practice which provides a relatively polemical allusive imitation of another cultural production or practice".[1] The literary theorist Linda Hutcheon said "parody ... is imitation, not always at the expense of the parodied text."
The [Britannica article](https://www.britannica.com/art/parody-literature\) reads:
parody, in literature, an imitation of the style and manner of a particular writer or school of writers. Parody is typically negative in intent: it calls attention to a writer’s perceived weaknesses or a school’s overused conventions and seeks to ridicule them. Parody can, however, serve a constructive purpose, or it can be an expression of admiration. It may also simply be a comic exercise. The word parody is derived from the Greek parōidía, “a song sung alongside another.”
...
... Miguel de Cervantes also took the romance as his target in Don Quixote (1605, 1615), while François Rabelais parodied the Scholastics in Gargantua and Pantagruel (1532–64). William Shakespeare mimicked Christopher Marlowe’s high dramatic style in the players’ scene in Hamlet (c. 1599–1601) and was himself parodied by John Marston, who skewered Shakespeare’s poem "Venus and Adonis" with his "The Metamorphosis of Pigmalions Image" (1598).
The page "Parofy from Literary Terms] reads:
A parody is a work that’s created by imitating an existing original work in order to make fun of or comment on an aspect of the original. Parodies can target celebrities, politicians, authors, a style or trend, or any other interesting subject.
The definition from The Free Dictionary reads:
1.a A literary or artistic work that uses imitation, as of the characteristic style of an author or a work, for comic effect or ridicule. ...
3. Music The practice of reworking an already established composition, especially the incorporation into the Mass of material borrowed from other works, such as motets or madrigals.
Thus a parody is often created with comic or humorous intent, but need not be. A work that imitates another in order to make a serious comment or criticism of it, or a serious comment on some related topic is still a parody.
A mention of or quotation from an existing work would be a literary allusion.
I do not see the need to coin a new term, particularly one likely to be confused with an existing widely used term, as the use of "tragedy" as suggested in the question would be.
The thing is that parodies are generally targeted at specific works, or at least at coherent bodies of work. Batman is a large corpus, having many different takes; a parody would pick out one version and parody that. Merely doing a different take on the Batman mythos is not doing a serious parody of the comic versions.
When a work targets comic or light-hearted works to show them in a more serious light, this is generally called deconstruction. Taking one of the more light-hearted version and showing, perhaps, that Robin would end up with Post-Traumatic Stress Syndrome as a result of having been, effectively, a child soldier.
