Some background and more than you need to know. But it does help explain the situation with exclusive mode and ASIO and how DSD fits in.
ASIO is used primarily for professional environments using DAWs (Digital Audio Workstations) for music production. One reason it is used is that it was designed for low latency. In this environment, it is quite common to have multiple devices hooked up. Therefore, it is almost always operated in shared mode.
ASIO has been adopted for "native" DSD in the consumer market, primarily because of its specialized handling of the DSD format, something that Windows and Apple do not handle well. The DoP format (DSD over PCM) was designed to handle DSD through standard Windows and Apple interfaces, but unfortunately the OSs does not handle higher DSD sample rates well in DoP format. Therefore, ASIO is used especially for higher sample rate DSD.
Each DAC manufacturer customizes the standard ASIO driver for its specific DAC and some have elected to use exclusive mode and some have not. In general, it has little to do with the actual playing of the file. ASIO, by design, bypasses the Window mixer, so exclusive mode is not needed to do that.
DoP format packs 16 bits of DSD data into a 24 bit PCM packet. The other 8 bits are used to identify the packet as DSD data. "Native" DSD packs 32 bits of DSD data into a 32 bit packet. It uses a separate signal to identify that DSD data is coming, rather than including that information in each packet. The 32 bit format used for "native" DSD is not supported by Windows or Apple, so ASIO was customized to support that format.
DoP requires 4 24 bit packets to send 64 DSD bits (4x16). "Native" format only requires 2 32 bit (2x32) packets to send 64 DSD bits, so it can use half the PCM sample rate that DoP uses.
Many people seem to believe that "native" DSD is sent as single bits at the DSD sample rates over USB. That is not the case. It is packed into these specialized 32 bit packets that ASIO can send and receive over USB at PCM sample rates. That format requires specialized handling which is done by the ASIO driver.
All of that helps explain why ASIO is used for "native" DSD and why ASIO very often uses shared mode rather than exclusive mode.
And, yes, it is a lot more than most people need to know.