There is a huge political difference between OCI and a Chinese travel document. A CTD explicitly lists the bearers nationality as Chinese.
An OCI card, as you said, is effectively like a PR card for former citizens. It is explicitly not citizenship politically and India fully recognizes their foreign citizenship.
If an OCI holder with a US passport gets arrested, India will notify the US consulate as they are a citizen. The same would not apply for a Chinese travel document holder. That is what I meant as “treated as a citizen domestically.”
As to political rights, I assume in practice that one cannot join the Party without first revoking their other citizenship, if at all. But since it is not a democracy, that was never a right/element of citizenship in the first place.