Based on the context during the stream, a vector quest is a quest pointing the player to a different location, likely named after the mathematical vector, a geometric object with length and direction.
In the base game, you often cannot start a quest at a location until you complete a prior quest at a different location. For example, you cannot start "Heart of Evil" at Jackdaw Cove in Bangkorai without completing "Imperial Infiltration" in Evermore. If you travel to Jackdaw Cove, you'd see it had a black marker, indicating there's a quest you need to finish to complete the location, but you wouldn't actually be able to start any quest, since the associated quest has a prerequisite. This could be confusing, since it's not immediately clear you need to go to a different location, complete a quest or series of quests there, then return in order to receive the quest that will complete the location objective. So, you instead find an NPC who offers you a quest that consists entirely of talking to an NPC at the location where the prerequisite quest is located. The idea is that you'll accept this vector quest, travel to the location, and pick up the prerequisite quest "naturally."
For the Jackdaw Cove example, if you go to Jackdaw Cove prior to completing "Imperial Infiltration," you can pick up "Dark Wings" from Wyress Freyda, which sends you back to Evermore. You often see confusion regarding this quest, because addons that show quests you haven't completed erroneously include vector quests (which become unavailable if you complete the prerequisite quest) and the description given on UESP--"Convince a former Wyress to leave the city."--sounds more involved than it actually is.
In the stream, I believe that the developers' definition of "vector quest" probably includes quests which can be started outside their associated zone. For example, Sorinne Gaerard will offer you "Tales of Tribute" in several cities, which sends you to High Isle to talk to Brahgas, but you can also begin the quest directly by going to High Isle and talking to Brahgas without being directed to him. My understanding based on the stream was that the vector portion of the quest--finding Sorinne in various cities--would be disabled until a certain level, but that if you knew about the quest beforehand, you could simply travel to Brahgas directly at any level.