Do 64-bit CPUs consume more power than 32-bit ones?
Does this mean that 64-bit CPUs consume more power in general than 32-bit ones, or have I misunderstood the results?


You're misunderstanding the results.  They're saying that 64 bit multiplication uses more power than 32 bit multiplication - which is true since it has to do more work.  However, doing a 64 bit multiply on a 32 bit CPU doesn't make that operation consume less power.  The same number of bits still have to be multiplied. Similarly, doing a 32 bit multiply on a 64 bit CPU doesn't necessarily consume more power.   


  Can we generalize and say that a CPU with a larger word size requires more power?


From that result, no, that would be incorrect.  However, in general it makes more sense to design higher performance, higher power CPUs to be 64 bit than 8 bit, so (for unrelated reasons) that will usually be true.