The narrator isn't named here (as of 10-13-16). A quick web search produced multiple sites saying it's Liev Schreiber but I'm 99% sure it's the same guy who narrates every documentary ever made :) It's been almost two years since I saw Tapia, but I can still remember what the narrator said at the end, and it's not Liev's voice I hear.
sharehttp://www.dailymotion.com/video/x2d4jq0_tapia-johnny-tapia-documentary-h-b-o-2014_sport
This is the full HBO documentary. At 51:05 you'll see "Narrated by Liev Schreiber" but that is definitely not his voice. Right? Also, it's not listed on his IMDB page with the other things he has narrated. Maybe he agreed to do it and then changed his mind so HBO replaced him with the guy who narrates everything else but forgot to take his name off screen?