Based on a bit of googling it would appear that PNGs don't have layers, but through the use of ancillary chunks Macromedia/Adobe Fireworks is able to save layer data. Unfortunately this data is specific to Fireworks, and so no other programs know how to use it; the same goes for state, and page data. I would assume this is probably why in the export options it's called a Fireworks PNG. Other applications also use ancillary chunks for their own purposes.
The PNG format consists of signature, and a series of data chunks. The signature lets the program know that this is a png file, and chunks store data. Chunks have properties to further define them. Byte 1 will define if it's data is critical, or ancillary. Critical means it contains data that is important, and if the image-software has issues with a critical chunk, it is required by the PNG specification to display an error message. Ancillary chunks contain data that isn't important to regular presentation, if the image-software cannot understand the chunk, or has an error it is allowed to skip the chunk. Byte 2 will define if it's private or public. Public means it's part of the PNG specification, and private means the data is specific to a third party. Byte 3 is just a reserved property for future revisions of the PNG format. Byte 4 defines if it's safe-to-copy, or unsafe-to-copy. This byte is for image-editors to tell one another if data in a chunk should be included in new images derived from this image. The idea being that some data may be dependent on other data in the image, and therefore would not work with a new image. Since the image-editor may not be able to understand the chunk this property lets it know how to use the chunk.
While I cannot find any information from Adobe/Macromedia I would assume that the layer data created by Macromedia/Adobe Fireworks is stored in chunks that are marked as ancillary, private, and possibly unsafe-to-copy. You will need to download Macromedia/Adobe Fireworks, install it, open the image files, and export them in a different format that supports layers; it should be a format that GIMP also supports. The common recommedation appears to be PSD, and to my knowledge that's the only layered format that Fireworks supports.