Why does benzene bend in this reaction?
That diagram is misleading because it’s technically in reference to bis(hexamethylbenzene)ruthenium(0). This is a famous example by the late and great E.O. Fischer. This Ru(0) complex is 18e, three methyl resonances were observed for the bent ring at −10 °C. Crystallography later confirmed this. This structure is surprising to the new student, perhaps, because the classic 18e bis(benzene)chromium is sandwiched between two planar arenes.

This is not an organic chemistry question. It is deep in the realm of organometallic chemistry, with a proper explanation requiring a molecular orbital energy diagram and then one has to invoke a Jahn Teller instability argument that requires lowering symmetry from $D_{6d}$ or $D_{6h}$. Suffice it to say, stability is increased by changing the hapticity.