All this information is available in Form F-1. The section relevant to your question is the Description of American Depositary Shares. This section contains a summary of the Deposit Agreement. Excerpt:
Deutsche Bank Trust Company Americas, as depositary, will register and deliver the ADSs. Each ADS will represent ownership of 160,000,000 Class A ordinary shares, deposited with Deutsche Bank AG, Hong Kong Branch, as custodian for the depositary, assuming the underwriters do not exercise their over-allotment option. Each ADS will also represent ownership of any other securities, cash or other property which may be held by the depositary.
To answer your questions:
NIO is special in the sense that there seem to be no "real shares" on any other exchange (Shanghai, Hongkong etc.)
The underlying securities are real shares (160,000,000 Class A ordinary shares), but these underlying securities do not publicly trade on any exchange. The "special" part you are referring to is that the underlying shares are not publicly traded. Even if the underlying shares are not publicly traded, the underlying shares are still "real shares".
My question is, if one owns these NIO ADRs, does one actually own part of the company or is there some custodian bank that owns the real shares?
The answer to this question is the same as the answer for all other ADRs: the custodian holds the real shares, while depositary receipts backed by those real shares trade on the exchange. Details are in the Deposit Agreement (an exhibit of Form F-1).
In other words, is there an additional layer of indirection of ownership?
As you can see, the "indirection" is not more than most other ADRs. The only difference here is that the underlying shares are not publicly traded.