It is believed that the use of such screenshots in the Doom Wiki qualifies as fair use because:
No freely licensed alternative exists or could conceivably be created.
The screenshot is used to convey ideas which cannot be adequately represented by text alone, as part of a scholarly discussion about some aspect of the game. The image is never used in a purely decorative manner.
The screenshots included in the Doom Wiki represent a trivially small portion of the original copyrighted media, which in no way replaces the reader's experience of playing the game. Therefore, their reproduction here does not infringe on the market role of the copyrighted publication.
The image was extracted from the game by the person who uploaded it.
The graphics are unmodified from their original form, possibly excepting simple labeling and scaling.
For each image on the Doom Wiki, an associated description page attributes its source and details the rationale for fair use of copyrighted material. This description page is easily accessible whenever the image is presented in an article.