Why do optical interconnects require less power than electrical?
It helps to watch the presentation starting at least as far back as https://www.youtube.com/watch?v=GcNyyeAeoJ8#t=2785 to understand what the premises are for that awesome slide in the question. The assumption, but not fact is that in 10 years time there will a reduction of 1000x in the power used by hybrid microring, silicon lasers; essentially these are lasers built straight onto the Si wafer and their hope is that in 10 years these lasers will be much smaller and use 1000x less power than the current experimental devices. Assuming that happens, then you'll see the awesome power reduction in supercomputer/cluster interconnects using optical interconnects based on such lasers (from the slide posted here). I'm no expert on lasers (in general), so I can't say if that 1000x reduction in power in 10 years is a reasonable prediction for such devices, but their hope appears predicated on an analogy with other silicon photonics (non-laser) device improvements, which apparently have reached that level of efficiency; that is made more clear on the subsequent slide https://www.youtube.com/watch?v=GcNyyeAeoJ8#t=3259. Presently these lasers appear to be not much better than using copper if the black lines are for copper in that slide (which is unclear). Frankly hoping for more depth of answer here on SE is a bit unreasonable, given that there only a few experts on hybrid silicon lasers in the world (the researchers actively engaged in this) and even they are making predictions rather than going by present day tech for those improvement claims...

Although I know little about lasers, I do have hands on experience in supercomputing [which is frankly why I got interested in this question], and based on my experience I'm rather skeptical of 1000x speed/power improvements in interconnects 10 years from now...