I’ve checked the data set and it indeed contains Analyze images. They are loaded into Slicer without problems.
Make sure to have the entire image (.hdr and .img files) available in the folder and open the .hdr file.
When you load the segmentation (Organ*.hdr file) then choose Segmentation in the Description column to indicate that it is a segmented structure (it will make it appear nicely overlaid on the image).
The .cls files describe label names and colors. You can manually edit the file in any text editor to bring it into Slicer’s .ctbl format. If you save that .ctbl file and load it into Slicer then after that when loading the segmentation file you can choose that .ctbl file in the Options column, which will make the segmentation loaded with correct segment names and colors.