So what is "Eucharistic service"?
I don't know if that's an official term, I suspect not. Under "Eucharistic services", I suppose you could group together the Liturgies but also rites like the administration of Communion to the sick and homebound, "Typika with Communion" (I don't know if there is such a thing officially, but I've heard of it being done here and there in rare circumstances), etc. All Liturgies would be "Eucharistic services", but not all "Eucharistic services" would be Liturgies.
How much of the reticence to ascribe "Liturgy" status to the Presanctified on the basis of a lack of consecration has to do with the difference between Slavic and Greek views of whether the wine gets consecrated? The latter view is that the Body sanctifies and consecrates the wine to become the Blood, which is an atypical form of consecration, but a consecration all the same. This is the same principle behind the Syriac Orthodox equivalent of the Presanctified Liturgy, called Roshem Kozo
(The Signing of the Chalice): the wine in the chalice is blessed by the Body, a fraction of which is immersed within it, effecting the consecration. If the Slavs adopted a more Western view leaning toward non-consecration of the wine, I suppose that's another way of looking at it: whether or not it's correct, however, has no bearing on whether the service is considered a Liturgy. The service books themselves describe it as such.