I have created a PostScript file from a TIFF image using ImageMagick.
The command-line I am using is:
convert input.tif[0] -density 600 -alpha Off -size 5809x9408 -depth 16 intermediate.ps
This takes my input tiff image (just the main image, and not the thumbnail via using [0]) and creates a .ps file from the bitmap.
When I look at the header of my PostScript file, I can see that it has the correct page size:
%!PS-Adobe-3.0
%%Creator: (ImageMagick)
%%Title: (intermediate.ps)
%%CreationDate: (2017-05-22T08:43:44+10:00)
%%BoundingBox: -0 -0 697 1129
%%HiResBoundingBox: 0 0 697.08 1129
%%DocumentData: Clean7Bit
%%LanguageLevel: 1
%%Orientation: Portrait
%%PageOrder: Ascend
%%Pages: 1
%%EndComments
Yet, when I use GhostScript to convert this to a PDF, unless I go to a lot of trouble to specify otherwise, gs is cropping it and putting it on a US Letter sized page.
gs -dPDFA=1 -dBATCH -dNOPAUSE -sDEVICE=pdfwrite -sDefaultRGBProfile=AdobeRGB1998.icc -dOverrideICC -sOutputFile=output.pdf -r600 -P PDFA_def.ps intermediate.ps
When I open the resulting PDF, the crop box is 612 x 792 pt which is US Letter. It should be 697 x 1129 pt, the size of the Bounding Box in the PostScript file.
I have created a custom .joboptions file using Acrobat Distiller that sets image compression and the like, and in this file if I specify the page size at the end, then the resulting PDF comes out the correct size:
<<
/HWResolution [600 600]
/PageSize [697.080 1128.960]
>> setpagedevice
Now this isn't a huge issue for a one-off conversion, but I have to convert a large number of images and I don't want to set the page size manually for every single file.
The lines you quote above are comments and, from the comments present, suggest that this is an EPS file, not a PostScript program.
The main difference is that EPS is 'encapsulated' which means its intended to be placed verbatim inside a PostScript program. The enclosing program contains the intelligence regarding the media size, and arranges to set the context such that the EPS is scaled, rotated, translated so that it fits appropriately on the media.
In order to do this successfully, the EPS file must follow certain rules; in particular it must not set any media size itself (because that would mess with the enclosing program).
So it seems likely to me that what you have is an EPS file which does not request any media size at all. So its hardly surprising that you have to tell Ghostscript what you want to do with it.
Now in order for the enclosing program to place the EPS it needs to know its characteristics, the size and shape of the content. That's what the comments are for. Ordinarily an EPS file is read by an application (eg MS Word, LibreOffice etc) which parses out those comments and uses the information when generating the final PostScript program. The reason an EPS uses comments to store this information is precisely so that it has no effect on the actual content of the EPS and so the entire EPS can be included without further processing by the application.
The short answer is that if you read the Ghostscript documentation here you will find descriptions of the EPSCrop and EPSFitPage command line switches which will do all the work for you.