DISCLAIMER: I have included a couple of quotes below, the first one is pretty hard to understand if one doesn't know the lingo. The second one makes a bit more sense.
To put it simply (I may be wrong, but I think I got the idea) "parasitic verb" is a metaphoric expression, not much used in philologist/linguistic realms (as far as I know) but that refers to "one verb depending on another" (like a parasite, "an organism that lives on or in an organism of another species, known as the host, from the body of which it obtains nutriment.") So, when you have "ha habido" "ha jugado" one of the verbs is parasitic to the other, "ha" would "depend" on "habido"...
Googling along, "parasit verb" has no hits, and "parasitic verb" appears in some Swedish linguistic paper... Boy, oh, boy... if you want a linguistic-cryptic "explanation" (with big quotation marks), and if you are better cryptologist than Sophie Neveu, then you may be able to get something out of the following...
(supine below, most likely refers to a construction such as "had played")
(QUOTE)
The parasitic supine construction displays the properties that are relevant for such a separation: a clear-cut discrepancy between form and meaning. The construction type exemplifies a complementation strategy available for a restricted class of infinitive selecting verbs in variants of the Scandinavian languages. The complement verb surfaces with an inflection identical to that of the matrix verb, yet the form has no effect on the interpretation, which remains the same as for the infinitival counterpart used in the standard language. The approach makes use of grammatical feature underspecification, the seeming gap between meaning and form being bridged by selectional restrictions and constraints on the relevant syntactic configuration. On the basis of its distribution, it is proposed that the phenomenon is a restructuring effect. The form is the result of morphological manipulations of the underspecified syntactico-semantic structure, providing it with the necessary clothes for Vocabulary Insertion.
(END OF QUOTE)
Don't you get it? (My own answer is, NO.)
So, I got the next, that finally explains it to me! (Hallelujah! = praise ye Yahweh!)
(QUOTE, again by Anna Lena Wiklund) (
bold not in original)
The purpose of the present study is threefold. Firstly, I wish to investigate the phenomenon of double supines in colloquial Swedish. In doing so, I hope to achieve my second purpose, which is to take a first step towards a better understanding of a particular kind of complementation of which the double supine construction forms a subset. I will refer to this complementation as
parasitic complementation. A parasitic complement has at least two characteristic properties: (1) The expected infinitival verb form that is prescribed in the corresponding standard construction is replaced by a surface form, where features seem to be copied from an adjacent superordinate verb. (2) The overt morphology of the
parasitic verb never has any influence on the LF interpretation and appears to be purely cosmetic. The present study is restricted to Swedish complements of modal verbs (bare complements)
where the complement verb is parasitic on a superordinate verb in the past participle form used in perfect tense formation (the so-called supine form). I refer to this as the
parasitic supine construction.
(UNQUOTE)
I hope this may shed some light.
Pero si tuviese más tiempo, no lo dedicaría a las sanguijuelas...