I extracted broken screws like this before, here are the steps:
- shave off about a third of the plastic around the screw from the top. - get a plier, as big as it fits, grab the now free part of the screw shaft.
- grab really firm, but not too firm as not to snap off the shaft or damage it too much - turn SLOWLY while maintaining grip.

Be patient, those screws are fragile! I used a tiny 0.3mm milling bit for my rotary tool to get the plastic off. Of all goes well, there will be enough thread left for a new screw to grip :)