Amniota is a crown-group; there's technically no such thing as a "stem-amniote", because if it's on the stem, it's not an amniote. The paper finds the diadectomorphs as non-synapsid theropsid amniotes, which is nice to have confirmed but isn't downright surprising (I found them there in my opus magnum, with weak support, and David Berman has been saying this since at least the early 1990s), but does not find the seymouriamorphs as amniotes, which isn't surprising either (aquatic juveniles, or in some taxa possibly neotenes, are preserved with external gills, and that's been known since 1945).
There is no good name for the amniote total group. "Amniotomorpha" would be obvious, but has never been published. People tend to go with Reptiliomorpha, a name published in 1934 explicitly in the context of amniote polyphyly...