Really late to the party here, but this has to do with dimensional analysis: https://quant.stackexchange.com/questions/66487/why-is-gamma-exposed-through-the-square-of-spot-prices?newreg=2569fe7d013140adb5880c6e344a4ba5

Now the next question is why he chose spot price. I'd assume the gamma exposure is based rather on the STRIKE price of that option, but I'm still investigating.