The issue is with your own interpretation of "compulsory". It means compulsory for anyone engaged in the activity being taxed. It's a tax on transit use rather than a tax on purchases or property ownership or what have you. Which is kind of a dumb thing to tax, but that's still what it is.
So by your definition, prior to the subway unification in 1940, paying the fare on the city-owned IND lines would be a tax, whereas paying the fare on the IRT and BMT was not?
Airfare isn't a tax, but Amtrak tickets are?
If I ride public transit in a foreign country, I'm paying a tax and the IRS will let me use the Foreign Tax Credit?
If I mail a package using USPS, that's a tax, but if I send a package using FedEx or UPS it's not?
No one I've ever met defines taxes that way. Nothing I've ever read defines taxes that way. If you want to convincingly define public transit fare as a tax, cite some reliable sources for this, because I literally can't find anything anywhere that supports this notion.
> If I mail a package using USPS, that's a tax, but if I send a package using FedEx or UPS it's not?
So let's get back to the word in dispute: compulsory.
What this means is, does the government service have direct competition? So the fee USPS charges for delivering packages isn't a tax, because you can have packages delivered by FedEx or UPS, and thereby subjects USPS to market competition and high prices or poor service would be met with loss of business. Use of USPS to deliver packages isn't compulsory. Whereas the price they charge for delivering first class mail is a tax, because the law prohibits anyone other than USPS from delivering first class mail within its jurisdiction, so then that fee is compulsory.
So, are road tolls a tax? Yes, because roads are a natural monopoly operated by the government and the fee is compulsory; there is no competing road network to use if you e.g. have to get your plumber's van to a customer site in lower Manhattan. Are transit fares a tax? Yes, for the same reason, when there is no competitive market for metro transit service; the only provider is the government.
You could make it not a tax by having competing private bus or rail service along the same routes, although if the government was charging money to the private buses or trains then the tolls would be a tax that the riders would ultimately be paying.
Which is why Amtrak tickets are a tax and airfare isn't, and also why airline tickets cost less than Amtrak tickets, when that otherwise makes no sense. The tax -- which causes the amount to be in excess of the price that would prevail in a competitive market -- being paid for Amtrak tickets makes them uncompetitive with airlines, even though they're not even direct competitors and trains should cost significantly less than planes, because being compulsory brings an inefficiency so large as to cross the gulf into a different market.
> If I ride public transit in a foreign country, I'm paying a tax and the IRS will let me use the Foreign Tax Credit?
IRS rules aren't exactly based on logic. For example, if a foreign government charges a tax to hotels that the hotel then incorporates into the price without explicitly listing it on the bill, are you paying the tax? Yes. Will the IRS let you deduct it when you stay in the hotel? That's a different question.
> No one I've ever met defines taxes that way.
How are you proposing to define it then? Give me a definition that can distinguish between paying the government when you ride the subway that they spend to pay for the tunnels and paying the government when you buy a sandwich that they spend to administer food safety regulations or prosecute anyone who tries to steal your sandwich.
I'm literally repeating what it says in the Oxford English Dictionary. What are you citing that equates transit fares with taxes?