Indeed
The confusion because "DenYoNet" seems to use a wiznet chip and also we talk about that. However it seems the details are different.
Yes, it's using the W5100

Even if it's done not in the memory mapped mode?
Yes, that doesn't matter. I developed the Wizenet code in a two-layer way. The lower layer is for writing/reading Wiznet registers and transfering data from/to the buffers. This layer is different for I/O and memory mapped, and has to be rewritten for different computer platforms. These are only a few and simple routines ("write byte to register memory", "write word to register memory", "read byte from register memory", "write data to buffer memory" etc.).
The higher layer code is handling the network activities like "open connection", "check connection status", "send data", "receive data", "close connection". It's still Wiznet W5x00 specific, but it doesn't know anything about how to access the registers and buffers, as this is done by the lower layer code. The higher layer code is platform independant when using the same Wiznet chip and it's probably even possible to use nearly the same higher layer code for both the W5100 and W5300 with small modifications for the register addresses.