The Coriolis force is definitely involved. Unfortunately, the English Wikipedia article is missing the explanation, but the German provides it:

The Barian wind law [Baric: something related to pressure] (also Buys-Ballot rule) by Christoph Buys Ballot states that the extended winds that blow from high pressure to low pressure areas are deflected, namely

• to the right in the northern hemisphere
• to the left in the southern hemisphere.

This is caused by the Coriolis force. In the northern hemisphere (the opposite is true in the southern hemisphere), it causes

• any mass that does not move parallel to the Earth’s axis of rotation is deflected to the right.
• This means that the air masses flowing into a low-pressure area rotate to the left (cyclonic),
• the air masses flowing out of a high-pressure area rotate to the right (anticyclonic).

The large-scale winds ultimately blow almost parallel to the isobars and can be calculated according to direction and strength from pressure differences and positions down to a few per cent. The underlying wind model is the gradient wind.