What constitutes a project to be a Bitcoin Sidechain?
A sidechain requires one or more blockchains, aside from the parent chain. This is different from off-chain, which is what would be the case in some types of Coinbase transactions. Since you didn't mention the presence of an additional blockchain in your other reference to a 3rd party which provides tokens in exchange for a payment, I would assume (albeit subjectively) that it would probably be an off-chain type of transaction in that example, too.

Rootstock, on the other hand, has its own blockchain, to create a 2-way peg with Bitcoin to facilitate smart contracts and other potential features, like near-instant payments.

Here's more information about sidechains in case you'd like to read about them in more detail. There are additional technical components beyond the presence of one or more blockchains:


Enabling Blockchain Innovations with Pegged Sidechains
A Simple Explanation of Bitcoin "Sidechains"