Learn Russian: Вино гонит прочь печаль.

Why does this sentence use the unidirectional verb гонит (гнать) rather than the multidirectional гоняет (гонять) for a metaphorical action?

When used metaphorically to mean 'chasing something away', Russian treats the action as moving in one specific, continuous direction (away from the subject). Because there is a single clear direction of movement, the unidirectional гнать is required here.

Does гонит on its own mean 'chases away', or is прочь doing that work?

Гнать on its own simply means 'to drive', 'to herd', or 'to chase'. To specifically communicate that you are chasing something away, you need to add the adverb прочь (away, out of here). The combination гнать прочь is the standard way to say 'to chase away'.

Печаль (sorrow) is the direct object here, so why didn't its ending change to show the accusative case?

It actually is in the accusative case! Печаль is a feminine noun ending in a soft sign (belonging to the 3rd declension). Because it is an inanimate object, its accusative form looks exactly the same as its nominative form.

Is it normal to split the verb and the direct object with the adverb прочь like this?

Yes. While Russian word order is flexible, keeping гонит and прочь right next to each other treats 'chases away' as a single, tightly bound action. Placing печаль at the very end of the sentence puts the dramatic emphasis on exactly what the wine is chasing away.