I really like to watch these too, but don't usually get to see them live due to work so I look for the recordings and find them hard to find directly if you don't know where to look. Also, on the twitch pages they have "Pinball Expo 2014" as the title for each of them and there is no description entered so you have to look at the date to know what to watch.
On the main page (http://www.twitch.tv/papatvpinball) there is no indication there are recordings available, and the 2 "highlights" posted link to 2013 Expo events...
from there you need to click on the "PAPAtvPinball" name to get to the profile page...
From the profile page (http://www.twitch.tv/papatvpinball/profile) you then see the "Past Broadcasts" link...
that takes you here (http://www.twitch.tv/papatvpinball/profile/past_broadcasts) where they are mostly all mislabeled as "Pinball Expo 2014"...
But, if you look at the dates you can figure out which episode is which and then you get to the good stuff (http://www.twitch.tv/papatvpinball/b/585723779).
You can also start at the PAPA site and link directly to each episode, but I think that takes a little time to get updated (http://papa.org/learning-center/video-resources/papatv-roadshow/)