It is my understanding that Platonic Philosophy is a form of theoretical gnosis, which is to say that it is a contemplative vision of reality expressed doctrinally - in Plato's case through the use of drama, symbol, and syllogism.
According to Plato, philosophy as such did not consist solely of its doctrinal expressions as represented by his writings. It was instead a comprehensive spiritual way consisting of contemplative disciplines, austerities, a religious foundation, and a form of initiation, all administered under the tutelage and companionship of a guide.
In his famous Seventh Letter, Plato wrote that none of his contemporaries would ever encounter a complete exposition of the doctrine committed to writing because a full understanding was only possible through a spiritual transmission made accessible through long association with a qualified guide and furthermore because the contemplative vision or intellectual intuition from which the doctrine arises is not capable of being reduced to exposition.
"Thus much at least, I can say about all writers, past or future, who say they know the things to which I devote myself, whether by hearing the teaching of me or of others, or by their own discoveries-that according to my view it is not possible for them to have any real skill in the matter. There neither is nor ever will be a treatise of mine on the subject. For it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself."
It is possible to reconstruct something of what this comprehensive way consisted of through recourse to the original writings and commentaries of Plato's successors, commonly referred to as the Neoplatonists and the fellowship behind Prometheus Trust has done a very remarkable job of piecing these fragments together - see especially The Unfolding Wings by Tim Addey.
Despite modern attempts to reconstruct the disciplines, including the practice of Theurgy, to the best of my knowledge, the spiritual transmission which Plato identifies as the key to the whole affair has not survived in its original context but rather seems to have been perpetuated within other traditional forms up to the present day, especially in the Islamic philosophical tradition in Persia.
To answer the question of the relevance of platonic philosophy today in the absence of a living form, I would say quite simply that it benefits those who are drawn to it as theory in the original meaning of the term. According to Frithjof Schuon in Tracing the Notion of Philosophy, "Theory, by definition, is not an end in itself; it is only — and seeks only — to be a key for becoming conscious through the 'heart.'" As an ancient expression of the perennial philosophy, it has the capability of informing our capacity for heart knowledge. I once obtained great benefit from the study of Plato's Dialogs which enabled me to discern the errors and inadequacies of modern pretenders to ancient wisdom by comparing them to the very fountainhead of wisdom in the West. Nevertheless the question then arose of whether I should devote my life to unravelling these ancient expositions, or more profitably spend my time investigating their contemporary counterparts which have the benefit of being attached to living and accessible traditional forms and spiritual ways. I believe that it is ultimately a matter of personal inclination and vocation but perhaps Plato's Philosophy, despite the undeniable benefits arising from its diligent study, is no longer capable of providing you with all that you are seeking to obtain from it.