This document summarizes HTTP APIs apart from SPARQL to access Knowledge Organization Systems. Good candidates to compare are marked bold.
There is a similar list at http://hypermedia.research.southwales.ac.uk/kos/terminology_services/links/ (needs to be checked for inclusion here).
Based on http://doi.org/10.5281/zenodo.61262 (limited to Open Source web applications). Atramhasis was not included in this list.
SKOS Editor, SISSVoc, and Ginco also provide APIs but they are not very well documented or just build on an existing API (SPARQL, OpenSKOS...). Among the remaining systems Skosmos and atramhasis cover most use cases.
Based on https://doi.org/10.5281/zenodo.166717 and BARTOC dumps at http://coli-conc.gbv.de/publications/bartoc/registries/. Also excluding SPARQL.