Having driven taxis in a previous life, I can tell you there are more different varieties of drunkeness than you can count. Happy, sad, morose, aggressive, quiet, the list goes on. The typical drunk, staggering and slurring their speech isn't the only way they behave.
The gate agent has only a few seconds with each passenger and is just trying to match passport, face and boarding pass so they can get onboard often under time pressure. Try getting into a nightclub at 2.00am on a Saturday morning and see how carefully the bouncers check to see if you're intoxicated. At that time of the morning drunks are not uncommon and the bouncers will have to deal with the problem themselves if they allow it inside.
Well done to the authorities for a fine of this magnitude, we need to see penalties such as this more often.