I don't know how it works in Vancouver but the answer in Toronto is yes, the cabbies get less when a fare pays by credit card. In the vast majority of company cabs the way it works is, the driver picks up a cab with a full tank of gas at the start of their shift, and returns it fuelled up at the end and pays a fixed rental fee, any fares and tips they collect over and above the fixed rental they get to keep but out of that they must pay for gas and other expenses (usually they are required to pay for a car wash at the start of the shift).

The larger companies that take corporate accounts and credit cards have a process where the cabbie turns in the slips and gets a credit, but not for the full amount, the taxi company withholds a percentage to cover both the credit card fee and their handling, in some cases the handling fee is a fixed amount so smaller fares are punished, these are high risk transactions so the banks charge cab companies the highest possible fee (those that require a validation by radio or by prearrangement probably pay a little less). It's a mild annoyance for the full time regular drivers, it's a pain in the butt for casual drivers.

I know sometimes I've been caught short in a cab too but honestly, do yourself a favour and stop at the ATM on the way out of the airport.