Shakespeare...Anime Style

Yes, this IS what you think it is: an anime based on Romeo and Juliet called Romeo x Juliet. As Wikipedia says, it's LOOSELY based on the Shakespeare classic. These videos feature the famous balcony scene and the opening credits to the show (I tried to put them together and upload it, but it failed, so it had to be two videos). Just one look at the opening and one can see why "loosely" is such an important word. If I may again quote Wikipedia:
In the fantastical aeropolis of Neo Verona, the noble house of Capulet had ruled peacefully for generations - until fourteen years ago, when the ancient grudge held by the rival house of Montague led to a mutiny, and the Capulets were deposed and all wiped out in a bloody coup. Now, as Neo Verona suffers under the thrall of its new masters, the fates of two star crossed lovers are about to become tragically entwined... As the citizens of the city suffer, the Capulet clan struggles to strike a blow against their enemies, and the Montagues tighten their grasp on power, an unlikely love blossoms between Romeo and Juliet - but in the face of such adversity, this ill-fated love may be doomed from the outset. Triumph or tragedy; only fate knows what awaits Romeo and Juliet...
I just love the flying-horse-beast-thing in the opening that looks like Falkor from The Neverending Story. Plus, that Romeo's got some pretty impressive jumping skills. But, all joking aside, I find it amazing and yet expected to see something like this. Shakespeare completely transcends cultures and time periods, allowing something like anime to reproduce his work (albeit LOOSELY) successfully. Look also at Romeo + Juliet and West Side Story to see examples of the play in different cultures and time periods. Of course, all of the plays we have read this semester can be easily placed in different time periods or cultures. For example, Toshiro Mifune starred in an adaptation of Macbeth called Throne of Blood, which was set in feudal Japan. A movie called My Own Private Idaho, starring River Phoenix and Keanu Reeves, is based on both Henry IV plays and Henry V, but it is set in the 1990s and takes place in Idaho and Italy. Finally, the Akira Kurosawa film Ran is based on King Lear, but set in the Sengoku era of Japan. Shakespeare's plays can easily fit any culture, time period, and medium and still make complete sense because his themes are timeless.
My questions about these clips are:
1) Does this anime represent an acceptable adaptation of Shakespeare? It may not be completely faithful, but is it right to put Shakespeare in anime?
2) What about Shakespeare's themes is timeless? Does that timelessness come through in these clips?