The extra contacts on the Canon hotshoe are to allow the flash to communicate with the camera, in order for the flash to read camera settings (such as the lens focal length to set the zoom factor) as well as access to the camera's light meter to perform automatic TTL (through the lens) flash metering.
To simply fire a flash in time with the camera shutter you only need two contacts. Your flash has two contacts, the centre one you refer to, and one on the side of the dovetail that makes contact with the hotshoe rails.
In the olden days the hotshoe was a simple mechanical switch that closed when the shutter mechanism moved. Nowadays it's electronically controlled. This means you should be careful when using old flashguns on camera as the voltage of the flash trigger circuit can be several hundred volts, which can damage the camera. In this case the use of a wein safesync or similar is recommended.
The camera's popup flash is only required to communicate with off-camera flashes. When using a third party flash on the camera hotshoe you should not raise the built in flash.