Venmo is owned by Paypal. Zelle is owned by all of the big banks collectively (Bank of America, Capital One, Wells Fargo et al.). The closest thing to a "small" player is the Cash app, owned by Square.
No commentary on the larger picture here or Amex/Discover, just pointing out your other examples don't exactly fit your point fully.
Well. PayPal is a payment gateway/system where merchants and consumers can both use; it's serving the same role as Visa/MasterCard. Venmo is a bit off but once Venmo allows merchants as cash recipients, it will serve the same role.
