The software is the "primary component" but a service is far more than just a piece of software.
It's providing infrastructure for the software to run in, maintaining said infrastructure, providing support to customers, billing/accounting, hiring people to do all of that etc. I'd even go as far as saying that the software being hosted ifself plays no major role in the service part.
Sure, but that's exactly what people mean when they say FOSS service.
Regardless, that's not the discussion we're having. The point is that those services are free of charge, and you're not the product. And that a big reason for that is that they are FOSS services.
Arguing about what people mean is futile. The point the other poster is making, and you've now agreed to be true, is that FOSS is software and a service is a service.
Most services powered by FOSS offer a free service as a taster for the paid service. The money made in the paid service tiers pay for the free tiers. Hopefully.