A playboy, by recognized definition, is a man who is a pleasure seeker, wealthy, pays no attention to responsibilities, especially responsibilities in relationships, and has relationships with more than one woman at a time (Collins English Dictionary, Merriam-Webster). While we certainly know that Demetrius is wealthy, we actually cannot refer to him as a playboy because we see him take his prospective marriage to Hermia very seriously. In addition, we are actually never told his motive for changing from being engaged to Helena to pursuing Hermia. While it may be just for pleasure, his change of mind may also be motivated by reasons of finance or social status. Regardless, whatever his motive is, Demetrius has certainly succeeded in earning Egeus's respect, which is another reason we cannot call Demetrius a playboy. Playboys are never considered respectable individuals. However, while we cannot call Demetrius a playboy, we can certainly say that he is fickle.
We see proof of Demetrius's wealth and social status in the very first scene. Not only does Duke Theseus refer to Demetrius as a "worthy gentleman" (I.i.53), Lysander also refers to Demetrius's wealth and social status when he argues that his own wealth and social status are equal to Demetrius's, as we see in Lysander's lines, "I am, my lord, as well derived as he, / As well possess'd" (101-102). Demetrius's wealth and social status are qualities that do fit the accepted definition of a playboy, yet the fact that he is respected disproves the assertion that he can be seen as a playboy. We see that both Egeus and Theseus consider Demetrius to be a "worthy" and respectable gentleman.
While it is questionable to refer to Demetrius as a playboy, we can note that his character is dubious due to his fickle nature. We can say that he is fickle because we see him, for no reason at all, transfer his affections from Helena to Hermia. Demetrius was even engaged to Helena before he began pursuing Hermia. However, after his experience in the woods, Demetrius now regrets letting go of his affection for Helena, as we see him explain to Duke Theseus in his lines:
To her[Helena] was I betroth'd ere I saw Hermia.
But, like a sickness, did I loathe this food;
But, as in health, come to my natural taste,
Now I do wish it, love it, long for it,
And will for evermore be true to it. (IV.i.172-177)
Hence, another reason we can call him fickle but not a playboy is that by the end of the play he has decided to be true to Helena once again.