at the end of the day, we measure time by the rate at which things happen. you can't measure time itself with a clock, because it's not fundamental. this is pretty non-controversial.
he makes a very interesting point that time is really a measure of gravity -- clocks (and nuclear decays and energy state changes, etc.) run slower in stronger gravitational fields. and this is essentially straight from special and general relativity, which give a special relationship between times and distances.
however, i think he's a bit premature in saying time doesn't exist. our best fundamental equations still fail us in significant ways (e.g. we have not been able to quantize gravity), and "time" could end up playing a more important role in resolving some of these issues than he thinks.
big picture: i'm all for any anybody that can get people talking and thinking about physics!