What are constructions like 'open-minded' grammatically? If you say they're paticiples I ask of which verb ('to open-mind' or 'to mind'? With which meaning then? Is there a meaning of 'to mind' like 'to provide a mind', 'to equip with a mind' or 'to have a mind'?). Or is it possible to form participles out of nouns with adjectives, too ('an open mind')?
We must start with a reasonably precise definition of 'participial adjective'.
Identifying a Participial Adjective
The participial adjectives are a major subclass of adjectives. They can be distinguished by their endings, usually either -ed or -ing. Exceptions to this rule of thumb include misunderstood and unknown, which function just like these other adjectives. They are called participial adjectives because they have the same endings as verb participles. [Obviously, adjectives ending in ed or ing that are not what we would class as -ed or -ing words, like red, are not in this subclass.]
Function in a Sentence
These adjectives are really meant to function like any other adjective: basically, they help to describe a noun. They might come from a verb form, or they might merely imitate the structure, but they always function as a descriptive adjective.
Note that there does not need to be a corresponding verb for a candidate to be classable as a participial adjective. OP himself has discovered talented, with no corresponding verb '[to] talent'. And note that 'They might come from a verb form ...' dismisses the possibility of back-formation of verb from adjective, which may well be a false assumption.
But does the class include compound adjectives where there is no corresponding compound verb (though there may be the corresponding simple verb)? OP gives the example open-minded, where the simple verb 'mind' (and the participle 'minded') exists, but not the compound verb 'open-mind'.
The article includes misunderstood with the corresponding compound verb misunderstand, which causes no problems.
But it also includes the example 'unknown', with no corresponding 'unknow'.
Though classification requirements are always a matter of definition, it looks to be most sensible to consider unknown, open-minded, open-mouthed, open-necked, action-packed, airheaded, middle-aged, widespread, windswept, eye-catching, death-defying, mind-boggling and so on as (compound) participial adjectives, even though no directly corresponding verb exists. Even with short-haired and the like, where even the simple verb needs searching for. But now someone will ask "And having put them in a nice niche, where has that got you?"