How to remove this screw?

You don't screw it out as such.

The drawer will pull out then you can gain access to the screw

If the drawer does not slide out currently have a look for other fixings either underside or other side of wardrobe

GreeBo has described it well, although I think it's called a cam lock rather than a half-moon nut. With it removed, the shelf will simply slide away from that screw (the hole that the screw fits through is big enough for the head of the screw to fit through comfortably too). I'm guessing there are probably two of them as well as a couple of dowels. It will be the same at the other end of that same shelf (out of view of the photo). The problem is that you can't slide the shelf away because it is also anchored at the other end. You say you can't access the other side of that screw because of there being another wardrobe there. How about the other side of this shelf? Is it the end panel of this wardrobe? Can you remove that? That's really the only way you can get the shelf off without damaging it

OP it will be something like this

100% is a cam lock, but I didnt want to add any confusion :)

OP your only option is to cut it out if you aren't going to remove the panels, however as standard60 points out you will be weakening the whole structure if you do this. Its adding as a shear support to stop the whole thing collapsing.

That said since, if I understand correctly!, its positioned between another wardrobe and a wall. So if you really want to remove it without taking it apart you either need to break/cut the panel or try to cut the dowel from the cam lock. Its chipboard, so even scoring one side of the shelf from the side to the cam lock hole is probably enough to allow you to break it by pushing from the side you just scored…

Then you could screw both side panels together with a connector bolt/inner screw such as below. (drill a hole through both panels, and put half of these through each side and screw together. This will have the benefit of stopping the robes from moving independently and allow you to line them up perfectly, if you so wish!

Also, be aware that there is more than likely a corresponding wooden dowel on the other end of the shelf. Typically its 1 cam lock and 1 wooden down on each side.

The back panel is typically some 3mm hardboard that has the same finish as the rest of the robe on the inside. It fits down a rebate in each side panel and often at the bottom/top panel. I would be surprised if you shelf is part of the back panel, though it may have some panel pins in it, depending on how it was assembled!

Think of a wardrobe as one of those collapsible storage boxes you get in IKEA, fixed shelves (and the back panel) stop the robe from doing what it naturally wants to do, which is collapse back to a flatpack :)

If you remove the "structural" shelf, the only thing stopping it from collapsing in on itself are the dowels and cam lock screws. They will be quite strong, but as you will see when you take the shelf out, the chipboard that they are in has very little strength to prevent the dowels/screws from simply breaking out.

If the robe was solid wood then it would be much stronger, even a cheap pine one would be stronger, but the long panels and short connection points between them mean you have huge leverage working to break them apart.

The cam lock is purely to make it easy to assemble and disassemble. You could break out the dowel in the same way as the cam screws. What is the back shelf support fixed to? If its part of the robe then it wont be going into the wall. Either way I would remove that as a first step.

Tbh, I would just pull the robe out from the wall and take it apart as it was designed! Yo have then thing empty already and they are quite easy to move.

You will spend longer trying to break it out and risk damaging the side panels and then have to pull it out anyway !

Are the top and bottom panels shared between the two robes? i.e. are they each 1 piece or 2?

If you look at the top panel, immediately above the double middle panel, can you see any evidence of fixings, and if so is there 1 for each middle panel?

Finally, are there already connector bolts/screws in the double panel?

The dowels are typically in the same, relative location as the cam screws, e.g. 5cm in from the edge.

You should be easily able to determine what the shelf support is fixed to by removing one of the screws, the length will tell you. You might also be able to see from above, as the back of the robe wont be tight to the wall, due to the side panels.

if they are separate then I would just pull out the one in question, remove the shelf as designed and then put it back in. Assuming its "wedged" into the alcove between the wall and other robe its not going to go anywhere.

Just be aware that, some other time you are doing something to it, once you take the back panel off it will likely collapse and break itself. If I ever have one in this state (which can happen during assembly) I try to keep from laying it with any panels flat on the ground, keep the edges on the ground to reduce the forces trying to break it.

Also keep in mind that the dowel(s) are often glued in with wood glue at assembly time.