Why does Google need Western Union?
They have a lot of money in the bank here in the US, and will also have a lot in money in the bank in all major countries where they do business. So the "sending the money" step can be skipped, they already have money in the destination country. If the service gets popular, they can always transfer in big chunks between their own accounts as required.
The only thing they need is a way for people to receive that money. They could partner with some big chain of stores that are widespread in a country, have people show up with a QR code or something like that for authentication, then get paid. They'd need to pay those stores something for their trouble, but it would be far less than what Western Union charges, that's for sure!