Tester is spot on about the lack of a neutral conductor, all you have is a hot and switched, the outlet doesn't have the necessary wiring. You'll need to run another line with a neutral. If that line also contains another hot then you can break off the tab between the two hot screws and wire the bottom with the new hot/neutral. If that hot comes from a separate circuit (not recommended), be sure to label this outlet as having two circuits inside so someone doesn't accidentally electrocute themselves. The best option is to fish a 3 wire bundle (plus ground) from the fixture light that contains the hot, switched (red), and neutral.
If you continue to use the existing wiring, I'd also double check that it's really a ground wire in the back of the box (in black insulation). It's entirely possible that you have an electrified box, in other words an electrocution hazard.
In the current form, electricity goes in the hot screw, and if something is plugged in the receptacle with the switch in the off position, it goes through the device, out the "neutral" screw, into the switch hot wire to the light fixture, and from there through the light and into the proper neutral. When two devices are run in series, you get a drop in voltage which is why you see the light fixture go out. And when the switch is on, voltage will pass through the switch rather than through the outlet since it's the easier path for electricity, powering the light fixture but not the device.