The camera does not need the shutter to open in order to meter the scene.

In an SLR/DSLR, light comes through the lens and is redirected by the mirror system while you compose through the viewfinder. A metering sensor reads some of that light before the exposure. In many designs, part of the light is directed toward metering and autofocus sensors. When you actually take the photo, the mirror flips up and those sensors are temporarily blocked, but by then the camera has already measured the scene and chosen or confirmed the exposure.

In mirrorless and compact cameras, metering is usually done directly from the main image sensor, since there is no reflex mirror blocking the sensor during viewing.

So the key point is: the shutter being closed does not prevent metering, because the camera meters using light available during viewing/composition, either via separate metering sensors (SLRs/DSLRs) or via the imaging sensor itself (mirrorless/compacts).