Not necessarily. The hangover is primarily a result of the first metabolite of ethanol, acetaldehyde. Some people (predominantly, but not exclusively, Asian and American aboriginal peoples) either lack or are deficient in the ability to produce the enzyme acetaldehyde dehydrogenase. That has two major effects: it encourages hangovers; and for those lucky enough to have the ability to metabolize acetaldehyde to an opioid analogue, it triggers the physical addiction cascade at a much lower level of intake. (Which, by the way, is why Antabuse is utterly ineffective in treating bafflingly hard-core alcoholics. It works by blocking acetaldehyde dehydrogenase, allowing toxic levels to build up in the system. It may bring on near-death hangover symptoms, but it also provides the fuel for an experience not entirely unlike mainlining heroin.)
"That's nothing." I very much disagree. "3-6 high alcohol beers" - do the math on the actual alcohol intake, on this.
The clinical def (of having a problem) is "more than two _drinks_ a day for men... more than four on a weekend binge..." or similar. The description is standardized and common.
Most people I find, who drink at the level of this fellow (something I've done, and could easily do again), are still deep in denial.
And yeah, you have to not only acknowledge your addiction, but also nail down what is about you, your genes, or your life, that drives you to seek that easy, frequent escape.