I’ve found this type (RRC 255/1) rather confusing for some time. It shows Hercules in a slow quadriga (associated with a triumphal procession) holding a trophy (a sign of martial victory) and a club (how we know which god is being represented). I just came across this entry in Pliny’s NH 34.16 and it seems to help connect some mental dots:
That the art of statuary was familiar to Italian Italy also and of long standing there is indicated by the statue of Hercules in the Cattle Market said to have been dedicated by Evander, which is called ‘Hercules Triumphant,’ and on the occasion of triumphal processions is arrayed in triumphal vestments;
To be clear, I don’t think the coin represents the statue, just that the statue helps suggest why this divinity might be represented in this type of chariot.
See Burnett 1986: 72 and passim for the assertion that Hercules at Rome is a god of victory.