Take a mental journey back to the 1960s. Most operators thought about game pricing as 1-coin/1-play, probably a dime for pinball. The "extra" chute lets them take in those higher-denomination quarters, which they would very much like to do. Further, they want to be able to take in a quarter regardless of whether the last game ended in a normal game-over ending (still fully powered), a tilt, or a slam tilt. The Bounce Switch and Anti-Cheat Switch seen on the bottom line cause what we now call a slam tilt, cutting off the R relay that energizes the 25-volt portion of the circuit.

Thus, inserting a quarter needs to re-energize the game if it had been slam-tilted or if this is the first activity since power was turned on at the start of the day. The W relay has to do some stuff up in the 25-volt zone: turn the score motor and step up the credit unit.

BTW, if you take a mental journey back to the 1950s, it would be a nickel in the 1-coin/1-play chute and 5 or 6 games from the quarter in the "extra" chute.
.................David Marston