It actually does fall under the definition malware. Specifically, Honey hijacks affiliate marketing tags and replaces them with their own. This falls under the definition of the “spyware” category of malware.

Spyware is software that sends information about the user (browsing history, etc) to a 3rd party.

Many affiliate browser extensions do indeed do this, as an extra revenue stream. In fact, I'd recommend never installing a coupon browser extension. But replacing one number with another does not meet the above definition of spyware.