Xenon is not a conductive gas until it is energized. A better explanation would be as follows.
The flash tube in a strobe has three wires - anode, cathode, trigger. The trigger is the coil wrapped around the exterior of the flash tube while the anode and cathode enter the tube at either end and make contact with the xenon gas. High voltage is applied to the anode and cathode but does not flow until current is also applied to the trigger. The trigger ionizes the xenon gas in the tube which then allows the current to flow from anode to cathode (or vice versa depending on which school of thought you subscribe to), producing an arc which we see as a strobe flash.