Like all forms of literature, poetry has evolved with the times, and I'd definitely agree that some contemporary poetry is influenced by modern technology and communication advancements.
Musicians as Poets
I wouldn't call musicians poets, just as I wouldn't call graphic designers, painters—they may be similar in some respects, but they're still ultimately different forms of artists.
I agree that some contemporary lyricists are poetic in their work; of course, I wouldn't consider Justin Bieber a poet, but lyrics by contemporary artists such as Nate Reuss (Fun.), Neil Hammond (The Divine Comedy), Jarvis Cocker (Pulp) and Nick Cave have come up with some brilliant, almost poetic lyrics recently.
David Bowie and Leonard Cohen, although not so recent, have also written some beautifully poetic lyrics in their time.
Contemporary Takes on Traditional Forms
E. E. Cummings is one example of a contemporary poet who has taken the traditional form of the Petrarchan sonnet and subverted and modernised it. His work speaks and challenges the conventions of the sonnet, and could be said to have modernised the form in his own way.
Rattle is a great site if you're looking for modern takes on traditional poetry. There are poems on this site that are written in traditional forms but address contemporary issues, and often subvert or play with the form in order to illustrate the point they're making in the poem.