Yes, drivers fund NYC street parking infrastructure.
NY state local roadway spending (streets, curbs, etc. used for the ~3M parking spots) is covered ~89% by driver-specific fees/taxes: gas taxes, registrations, licenses, tolls (Tax Foundation FY2023 data, latest detailed). General taxes cover almost none.
It means the parking spaces aren't "free" to society—drivers already pay nearly all maintenance costs via user fees, not broad property/sales taxes everyone pays. Current street parking is mostly unmetered, but the underlying roads aren't subsidized by non-drivers.