The whole entry sounds Stoic in character. As Diogenes Laertius 7.63 reports in the context of a Stoic doxography, gra/fw (“[I] write”) is classified as a verb, but it must be understood as an “incomplete expression”. See also sigma 1357, where the Suda speaks of a “quasi-event” (parasu/mbama) or “incomplete predicate” as a “thought that is not self-complete”. A “quasi-event”, though, is rather an impersonal verb with a dative depending on it, such as *)iwa/nnei me/lei, i.e. “to John there is a care for” (on this issue see, Ammonius, Commentary on Aristotle's De interpretatione 44.18-45.7, ed. Busse, included in SVF 2.184). The other important point is that in the assertion “John writes” the expression “writes” is not strictly the verb, but the signification of the “verbal sound”, which in this case is a “predicate” (kathgo/rhma). A verb is rather what signifies a “non-composed predicate”, i.e. a predicate in which the subject “I” is elliptical: “(I) write”, “(I) speak” (this is the Stoic canonical definition of “verb”, quoted by Diogenes Laertius 7.58 and, I think, closely connected with this Suda entry).
For further discussion see J. Barnes, “Language”, in Algra, Barnes, Mansfeld, and Schofield (1999), especially, 202-206. See also Long & Sedley (1987) vol. 1, 1999-202 and Frede (1994).