Hi and welcome to the forum!
(Background: I research motion events, but not specifically from a Talmy-style perspective.)
Talmy's original proposal was schematic, including several types of motion events. The current usage is rather stripped-down (read: oversimplified) from that, adopting the original schematic labels. Rather than just following from that narrow perspective, I'd recommend following Talmy in looking back at his earlier ideas. There are of course many publications on the topic, but here's a convenient overview from his perspective:
https://sites.google.com/site/coglingwroc3/plenary-lecture(Unfortunately it looks like at least for the moment the video is not loading from Youtube, so let me know if you want me to try to locate it for you to watch.)
Now regarding the terminology itself, consider especially the terms "verb-framed" vs. "satellite-framed", where "verb-framed" means verbs encode
path, while "satellite-framed" means verbs encode manner [
https://en.wikipedia.org/wiki/Verb_framing]. Thus
manner is secondary from the perspective of this typology, but
path is specifically defined. Path refers to a clear component of the motion event (=path, direction), while manner refers to more semantically full and variable ideas about how that motion is carried out, including attributes like speed, means/method, style, etc.
I would interpret this to mean that "manner" isn't a generalizable category from motion events to other event types, simply because it's basically the leftovers (or additional information) once path is specified. You could use the term analogically (either generally for 'additional information', or narrowly for 'how/manner') for other event types, but I don't see a clear/unique way to do that. I suppose there's some general relationship between the ideas of "complement" (generally obligatory, core arguments of a verb) and "adjunct" (optional modifiers), if we adjust those concepts from a syntactic to semantic level. So you could try to figure out the core event properties of various event types, then the rest would include "manner" (again, either narrowly or broadly).
Of course there are many other approaches that have proposed ways to analyze event types other than motion, so you might find those more useful for your question. Or you might just choose an analogous approach to Talmy's motion event types that fits your research well-- in that case just be sure to explain your motivation and methodology, and it should be fine.
So in short, your comments about Moline & Stosic (2016) seem appropriate to me. It's a complex concept with various dimensions (maybe not even enumerable). This also brings up a deeper question: what is the point of a typology like this? What kind of claim does it make? Is it purely descriptive so that it is convenient to compare English ("satellite-framed") to Spanish ("verb-framed"), thus highlighting an interesting difference between the languages? Or is it theoretical with some more concrete claim about how language works? Are these categories meant to be cognitive primitives (even part of Universal Grammar)? Or are they emergent? Generally speaking, Talmy's work seems to fit in well with a Cognitive Linguistics approach, which generally takes the perspective that linguistic phenomena are based on perception, experience and cognition, so that they are considered complex and emergent categories, rather than reducible to logical primitives, but at the same time the typology would at least appear to lend itself to a more categorical and absolute distinction between languages,
if that works out consistently ("universals" rarely do).