Capture the Flag is exactly as you'd expect, if you've ever played that type before. The object is to retrieve the enemy team's flag from their side and bring it back to your side; the team with the most points at the end of a predetermined set duration of time wins. The video shows off a few zones of combat that frankly appear very similar to each other, and could use a better color scheme to visually differentiate themselves.
The second of the two sample PvP game types is Team Annihilation, which is simply about killing other players. There is a slight level of tactics involved, and it centers around a totem statue, next to which players will respawn. If you're able to destroy the totem, players will no longer respawn, and that could very quickly end the game.
One interesting item to note is that Ellingsen mentions that playes will receive PvP experience points for PvP gameplay, which they will use to level up their PvP stats and purchase items and equipment. Presumably, this system will be separate from single-player stats.
The video ends with a quick teaser concerning guild vs. guild siege warfare, which Ellingsen says will be unlike anything ever seen in an MMO before, but saves the specifics for future episodes of the Hyborian Insider. So, if you're absolutely starving for more AoC details, you'll enjoy this video, but otherwise, keep counting the days until May 20th.