The company exists to minimise the cost of increasing the speed of a transaction with "gas fees". Sort of like when you pay for something with your debit card and then pay a second company to make the transaction go through in under a day.

Not what the company's website says (or means). Gaslite.org says they are a B2B company that helps make other companies' smart contracts more gas-efficent. So they look at code and say, e.g., "you can use a storage pointer here instead of copying to memory, and this will make it require less compute to deploy and run", and the client company implements those changes before deploying. The thing that determines transaction ordering is the price per compute. So users paying a higher per-compute rate on a transaction to jump the line is a very different thing than somebody changing their code to require less compute.

Anyway what that actually means is he's a freelance dev who will charge stupid companies a lot of money to run hardhat-gas-reporter on their code.