I took "tap to pay" being clicking on Order in an app; and I have certainly made a "online order" from inside the Chipotle, on their wifi with my laptop (usually because walking to the counter would cost more because of stupid promotions).
It makes more sense that they're referring to Apple Pay or similar shenanigans (which itself is more annoying than a credit card, to be honest, Face ID goes wrong or the double click closes the wallet app instead of authenticating way too many times, especially if you're trying to do it one-handed).
You seem to be part of the problem. As long as people like you are happy to run spyware on their phones for the sake of convenience or a meager discount, companies will be empowered to make such software and devices a requirement.
I use cash whenever possible, but carrying cash for larger transactions has its own risks and those risks need to be balanced against the privacy benefits it offers. The way I see it, carrying a credit card in addition to my phone when I might need it is a minor inconvenience relative to that of allowing Google complete control over my phone.