A bribe doesn't have to involve a government official.

A bribe requires three entities:

- the one paying the bribe (in this case the paper's author)

- the one receiving the bribe (in this case the journal editor)

- the one that actually provides the benefit (in this case the company that owns the journal)

What makes it a bribe is that, instead of paying the entity that's providing the service, you're paying an agent of the entity.

If you pay Harvard $1MM to admit your child, that's not a bribe. It's just a transaction. If you pay a Harvard admissions officer $1MM (to their personal account) so that they admit your child, that's a bribe.