In Goldberg's approach, "phrasal" only means that the construction is complex and is made up of multiple words/units. She does not assume a "phrase-structural" analysis, as she writes in her 2013 paper "Explanation and constructions". I think this has to be made more clear in the book. Here is a quote from her article:
"Argument structure constructions are phrasal in the sense that they are not zero level grammatical categories but rather consist formally of an array of grammatical relations such as subject, object and oblique. They may, but need not, specify lexical material as well. For example, the object grammatical relation may specify particular words (e.g. way).
At the same time, argument structure constructions do not specify phrase structure trees or word order directly (cf. also Osborne & Gross, 2012). Other constructions that they combine with do. In particular, a general VP construction specifies statistical constraints on the ordering of postverbal complements, dependent on weight and information struc- ture (cf. Wasow, 2002). There has been some misunderstanding about this in the literature, as it is sometimes assumed that ‘phrasal’ means that a particular tree configuration must be specified and that linear order is necessarily fixed in advance (e.g. Müller, 2006). But it is not necessary, nor advantageous to make this assumption."
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Regarding this part:
Remi van Trijp wrote:
Link to original comment. About docloop.