Only one fossil of the single and type species, D. angusticollis, has been discovered in deposits of the Early Devonian period (Emsian stage) in the Beartooth Butte Formation in Wyoming, in the United States.

The only known specimen of Dorfopterus consists of an incomplete uncrushed telson (the posteriormost division of the body), which was long, narrow, styliform and with a central carina ("keel").

Originally described as part of Stylonuridae by the American paleontologist Erik Norman Kjellesvig-Waering in 1955, the strange morphology and the little known fossil material of Dorfopterus have made the classification of this genus problematic.

[6] Dorfopterus' only known specimen, its holotype, was found on Lower Devonian deposits on the Beartooth Butte Formation on Wyoming, in the United States.

The first part of the generic name, Dorfopterus, honors the American geologist and Princeton University professor Erling Dorf, who discovered the Beartooth Butte Formation on 1934.

[10] During this study, Kjellesvig-Waering said that new specimens found by the American paleontologists Robert Howland Denison and Eugene Stanley Richardson, Jr. showed that Dorfopterus was a gigantic eurypterid whose reticulated patterns on the telson repeated on its opisthosomal (of the opisthosoma, its abdomen) tergites (the dorsal halves of the segments eurypterid abdomens are divided in).

[19] Dorfopterus would not be an exception to these changes; having only been assigned to Stylonuridae due to its long and narrow telson (even though no member of this family or of Eurypterida as a whole was known at the time to have had an ornamentation similar to Dorfopterus as Kjellesvig-Waering admitted),[1] the genus' classification within this family would be rendered as tentative in 1966 by Kjellesvig-Waering himself,[10] although it would be continued by the Norwegian paleontologist Leif Størmer during his 1974 revision of Eurypterida.

[20] In 1979, the British geologist Charles D. Waterston erected a new eurypterid family, Parastylonuridae, and included the genera Hardieopterus, Parastylonurus and, doubtfully, Dorfopterus and Lamontopterus.

[21] Waterston compared the rib-like ornamentation and carina ("keel") of Dorfopterus with the structure of the telson of Parastylonurus and assigned the genus to this new family.

[25] In 2007, Tetlie proposed that the fossil of Dorfopterus could represent the telson of Strobilopterus princetonii, then unknown in the latter except for a juvenile specimen in which it was poorly and fragmentarily preserved.

[24] To determine whether this was the case or not, he studied the only known specimen of Dorfopterus through a scanning electron microscope (SEM) and an energy dispersive X-ray analysis (EDAX).

This way, Tetlie was able to confirm that it was not some other organism such as a plant or a vertebrate animal that had been erroneously labelled as a eurypterid, but he did not manage to reliably ensure the classification of Dorfopterus within Eurypterida.

The cladogram below follows Plotnick's thesis, which has been simplified to only include major eurypterid clades and incertae sedis genera not pertaining to any of them.

The position of the genus on it holds no informative value regarding Dorfopterus though, as it was placed together with the rest of the genera Plotnick considered as incertae sedis at the top of the cladogram, without including it in any specific eurypterid clade.

[26] Furthermore, the internal classification and phylogenetics of eurypterids have been substantially revised since 1983, making Plotnick's cladogram greatly misaligned from current knowledge.

[28][16] Dorf interpreted the lithology (the physical characteristics of the rocks) of the place as being proper of a non-marine,[16] red-colored infilled channel[29] in which rocks were deposited in quiet, shallow and estuarine (proper of an estuary, the final part of a river that joins the sea and of brackish water) conditions,[16] with the environment possibly having been an estuarine channel.