Working with ArcGIS AIG Raster format

I downloaded a specific layer which has the format "AIG" as you can see in the screenshot.

It has no projection so I applied "Define Projection" on it. It seemed to work but nothing changed in the file and in its appearance. After that, I tried to convert it to a polygon and then define the projection. This time it changed in the layer but again nothing changed in ArcMap (and yes, I re-added it). I even change the format from "AIG" to "TIF" and "GRID" and then applied all but nothing changed.

I have various files to compare which all match with each other but this file simply does not do anything at all. I guess its because of the "format".I have never seen it (ArcGIS Binary GRID) and thats the only thing which is different from a normal raster file.

The site I downloaded this file was from a EU database so actually it should be fine and probably frequently used.

Do you have any experience in working with AIG Rasters? Is there another possible reason I forgot which could cause these problems?

Here is a screenshot of the layer (up-right) and UK (bottom-left, with right projection). You can see the offset.

Thank you, Patrick