I will relay some of my experience as a cellular retail service technician here.
Futuredial makes a product called Cellebrite (the UME-36 if I recall correctly), which is used by cellular retailers to transfer contacts between phones. The unit can use Futuredial-provided USB or serial cables to allow phones to be connected to the unit.
The software on the Cellebrite will read and write contacts to just about any relatively recent phone in existence (we had cables to connect to phones as old as the Motorola StarTAC). Contacts are read by the Cellebrite software, held in its RAM, and then written to the destination phone. Alternatively the contacts can be exported to an SD card or to PC software over a separate USB connection.
Many of these Futuredial cables will work on the PC if you can find the proper drivers. There also was PC software available that used the same or similar cables and performed most of the same functions as the Cellebrite, namely ICSS and SN-RMS. Frequently we would use Futuredial cables on the ICSS and SN-RMS software without issues, these softwares were bundled with a myriad of cable drivers (and many were just USB-to-serial interfaces, we had COM ports up to the 130's). The Cellebrite was much faster and simpler in most instances so we preferred to use that. Only ICSS and SN-RMS would do firmware upgrades, so that is why we needed it.
It's entirely possible the cable you've posted is just a charging cable and doesn't have the hardware within the cable to enable contact transfer.
However, in most instances on older feature phones, including the M300 if I'm not mistaken, when you connect it to the PC, you aren't given access to anything like a mass-storage mode, or anything that would make sense to snag contacts, but either a USB-to-serial interface where you are expected to send AT commands (like an external modem) or a proprietary diagnostic mode meant for firmware upgrades. The protocols for contact transfer on these older phones are completely proprietary and likely unique to each manufacturer and that's where reverse engineering projects like BitPim are needed.
I can't remember if BitPim supports the M300 but if you can get the Futuredial cable for it, you can use it with BitPim.
If it's a Sprint phone, try calling a Sprint service center to see if they can copy the data for you on an SD card. If they have the Cellebrite machine, which all repair centers do, it's a trivial matter to perform.
Otherwise, if I'm not mistaken, the phone does Bluetooth contact and photo transfer so you might just get a Bluetooth dongle for your PC and see if you can do it that way.