"Common Cathode" means that all the LED cathodes for each digit are connected together - they are "common"

Your schematic shows a Common Anode display; ie, all the Anodes for each digit are connected together:

COM1 connets to all the Anodes for digit 1;

COM2 connets to all the Anodes for digit 2;

COM3 connets to all the Anodes for digit 3;

COM4 connets to all the Anodes for digit 4.

You will be able to see this in the Datasheet for the display.

The 8051's ports are basically open-drain drivers, so they can sink current, but not source it. Therefore you really do need to use a Common Anode display.

An example of using a common-anode display is shown here:
http://chaokhun.kmitl.ac.th/~kswichit.../7-seg.htm

To use a common Cathode display, you will need driver transistors for each segment. You will almost certainly also still need a driver transistor for each digit - it is unlikely that an 8051 port pin can sink eanough current for all the segments in a digit (certainly not at 15mA per segment!)