The definition of "addiction" varies by field. In economics, "addiction" is the phenomenon of a behavior having increasing returns on investment. (Which means that if you do some, you'll want to do more.)

This has the disadvantage that it is near-totally unrelated to what most people think of as "addiction". But it has the advantage that it is a coherent concept, which isn't true of most offered definitions.

In the vernacular, "addiction" just means that you disapprove of someone's behavior.

In medicine outside psychiatry, "addiction" refers to the phenomenon of physical withdrawal symptoms in the absence of something. For no particularly good reason, you are not considered to be addicted to oxygen. But that's not part of the definition, it's an implied codicil.

Psychiatry defines a single "addictive disorder", which is compulsive gambling. Nothing else is considered addictive. This seems to be a response to the fact that no one has ever provided a workable definition of addiction. (See e.g. https://www.porticonetwork.ca/web/fundamentals-addiction-too... : "The term addiction is no longer used to describe substance use disorders. It was felt that the term was so loaded with associations that it lacked precision.") This comic ( http://www.smbc-comics.com/comic/2014-03-21 ) provides an amusing illustration of the issues. But for a less irreverent joke at psychiatry's expense, this formal paper ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5328289/ ) spends some time making fun of the fact that compulsive gambling is the unique "addictive disorder" while compulsive stealing, which is mostly identical except in the specific behavior expressed, is an "impulse control disorder".

Here's how the different systems classify caffeine:

Vernacular: addictive if you're a Mormon; not otherwise.

Economics: not addictive; no increasing returns.

Medicine: addictive. (Withdrawal causes severe headaches.)

Psychiatry: not a substance use disorder. (Consumption of caffeine may be compulsive, but it is not a "disorder", itself not a well-defined term.)

I suggest to you that the definition you provided, "a behavior that impairs other aspects of your life to a large degree", comes from psychiatry, but is actually part of the definition of a "disorder", not an "addiction".