Edit in response to new photo:
I think this is your problem. You've loosened the wrong bolt!
You've been looking at the pivot bolt(s), which just hold the stem together. To adjust the angle you need to loosen a bolt that you may not even have noticed, the one under the stem.
I strongly suspect that your stem works like the one below:
The bolt on the lower left holds the silver plate in place, and that plate has big teeth on it that lock into matching indentations in the stem. If you loosen the bolt the plate moves out letting you adjust the stem.
The rest of it is not really relevant any more, but I'll leave it in anyway.
Many of those stems have the "bolt" on one side of the stem fixed. Like the seatpost bolt in dlu's answer, you push it in and it locks in place. The seatpost one has a little tab, the step ones usually have a hex part under the head of the bolt.
The photo below shows a similar stem, only this one has a replaceable bolt where yours seems to have the bolt and cap and one piece ... the stripped piece.
That means that if the bolt is tight you can't rotate the bolt head by putting an allen key in and turning it. Only one side will turn, the other side will strip if you try. That may well be what has happened here.
I think the idea is that that side lets you hold the stem at the right angle while doing up the bolt on the other side (making it a two hand job rather than a 3 hand one). So if you've been trying to turn the wrong one you could end up stripping it.
The good news is that it doesn't really matter - that side is fixed anyway.
I think that if you push the "bolt from the back side" part it will slide out. You will probably need to lift the handlebar side of the stem a little to release the downward pressure on the pivot. Basically push and wiggle.
I would do that by screwing the bolt you have in your hand back in a little, leaving a couple of millimetres gap so that when you push on the bolt head there's room for the bolt to slide into the stem a bit.
With a bit of imagination, the top view looks like this. The blue is the stem, red is the fixed "bolt" with the stripped head, and grey is the short bolt you've been able to remove. If you push leftwards in the diagram the red bolt should slide out.
Alternatively, find a punch or a smaller bolt that will go into that threaded hold without damaging the threads, and use a hammer to tap the remaining "bolt" out.
There's two approaches: you want to keep the adjustable stem and ideally change the position, so you don't want to damage anything; you want to adjust it and if you can't you need a new stem, so if you damage it trying to adjust it that's no great loss. Obviously in the first case you can hammer that bolt to get it out, because either you move it or you're going to throw the stem out. But if you want to keep the stem more care is needed.
To me, those adjustable stems are not great and mostly should be used to discover which fixed stem you need. So I'd be inclided to force the adjustable stem a bit more.