The power flows through the cable, that's correct. However, the wrong assumption is that the clock is not part of the circuit, because it actually is!
If you stop the video linked by Paulie at the right moment, you'll see the lightning striking the highest point of the building (which actually makes sense):
As you see, the lightning strikes that small antenna or flag pole on top, not the pointers of the clock. The electricity then continues through the clock, over the hands and then the cable.
As such the whole energy is not diverted from the clock, but rather pulled through it directly.
If Doc wanted to protect the clock, he'd most likely been able to attach the cable to the flag pole/antenna instead, but it's also likely that this might have screwed the whole circuit, since we don't know the actual resistance of the clock compared to the cable and flux capacitor. Worst case it could have been that the clock provides a lower resistance towards ground, which would have caused most (if not all) of the electricity not going through the cable and time machine.
So the actual (simplified) circuit looks most likely like this:
Also note that despite Doc holding the cable, he's essentially short-circuited out (meaning there's essentially almost no potential difference between his hand and therefore next to no energy flowing through him), which allows him to survive this (at least on a Hollywood level of physics being applied, considering the halo around the cable, etc.). He's like a bird sitting on a power line.
Edit: After watching the scene over and over again (after reading Valorum's answer), I noticed that you can actually see that the top end of that cable is connected to another cable, which goes straight up to the antenna.
So it seems like Doc intentionally used the hands of the clock as some kind of cable relief (otherwise he would have unplugged it when he attempted to slide down).
Let's have a look at the updated circuit:
As you can see, this changes nothing for Doc. However, it changes a lot for the clock! Due to the clock now being parallel to the rest of the circuit, there'll be a most likely significant higher voltage and current involved now. Before the Flux Capacitor could act as some kind of current limiter, which is no longer possible. So based on the resistance within the time machine this could actually mean that most - and not just a bit - of the lightning's power interacts with the clock (read: destroys it).