Shakespeare is all about emoting; it was written for the stage, and requires an ability to project feelings and nuance through stilted language. Frankly, even modern English frequently sounds stilted coming from Reeves, let alone this. And it really doesn't help that he completely stopped even attempting the accent at 1:10 in that clip. Go on, listen to it again. They couldn't have tried for another take? Which raises a worse possibility: They did try over and over again to get a better take, and at a certain point each time, the part of Reeves' brain that controls his accents went from "Shakespearean" to "Can I get medium fries, please?"
But it's not just Shakespeare. Transport Reeves out of the comforting confines of the turn of the millennium, and he inherits all of the dramatic chops of a waffle. In the otherwise largely solid Francis Ford Coppola's Bram Stoker's Dracula, a terrible decision was made to put him up against Gary Oldman, and not just any Gary Oldman -- weird Transylvanian Gary Oldman:
Oldman's reaction at 1:18 is not part of the character. It's just him responding to Reeves' piss-poor accent. And frankly, he may have deserved it.
And then there was his small but distracting role in Dangerous Liaisons, where he was up against two of the greatest actors of their generation. We'll just leave this right here: