A dry vent is a vent pipe that is ONLY a vent, and does not receive drainage water from a fixture.
A flat vent is a vent that runs horizontal instead of vertical. The "break point" for a pipe being horizontal or vertical according to code is 45 degrees from level. If the pipe is 44.999 degrees from level, than it is still considered flat. 45 degrees or more from level, and it is considered vertical.
The section of 2" pipe that went horizontal is PROBABLY a flat vent. I can't know this for sure, as I didn't see the piping arrangement. This flat vent pipe needs to be washed through by another fixture unless it is 6" above the rim of the fixture that it is venting.