This is actually two separate scenes edited into one clip below. The first part takes pace at the 21 minute mark in the film and the second part takes place at 1:04:25.
The filmmakers clearly went out of their way to hide the particular brand here, so we'll have to put this in the "Mystery Malts" category. A closer look at the bottle shows that there is clearly no writing on the back label and only vague a Japanese logo on the front. The label looks similar to Yamazaki 12 year but the bottle design is quite different. Safe to say this is a made-up brand. Like Clyburn or MacCutcheon
Alonzo (Denzel Washington) asks Roger (Scott Glenn) for some of his "$300 a glass shit", So I doubt it is Yamazaki.
"Training Day" now available on Blu-ray