There's nothing about their own contribution.
They just take the existing approaches in BTC and ZCash, and just mix them together.
In Section 7. The Future of Bitcoin Private they stated that they will implement new techniques, from another projects, when they will be ready.
improving the privacy of Bitcoin Private is to utilize the “Dandelion” privacy project currently under development. This technique involves the “stem” (the transactions) and the “fluff” (obfuscation). While any obfuscation procedure is inherently less secure than zk-SNARKs, Dandelion obfuscation could be added to both transparent and shielded transactions of Bitcoin Private, improving privacy across the board.
We all agree that we need some privacy in crypto. But this privacy should be done by real developers and researchers, who can contribute something on their own. And it being done.