"Works with" has nothing to do with getting the 300 speed . Just means that it will pick up a signal from the router. The overview of the 160 specifically mentioned the 825 and 855 that's why I mentioned them.
This is right the DWA-160 product page:
* Maximum wireless signal rate derived from IEEE Standard 802.11g, 802.11a, and 802.11n specifications. Actual data throughput will vary. Network conditions and environmental factors, including volume of network traffic, building materials and construction, and network overhead, lower actual data throughput rate. Environmental factors will adversely affect wireless signal range. Wireless range and speed rates are D-Link RELATIVE performance measurements based on the wireless range and speed rates of a standard Wireless G product from D-Link. Maximum throughput based on D-Link 802.11n devices.