The main FRAGSTATS documentation has a section on the necessary format of the batch file, also in the tutorials package there is an entire section on batch processing, so I wouldn't really call it useless.
Each line of the batch file contains the path to the file, and attributes about the raster. Since you are using GeoTIFFs most of these attributes can be read automatically by FRAGSTATS. So really you just need to get a list of your rasters and output the paths to a text file. This becomes a fairly simple task in Python.
from arcpy import env
#Set workspace to folder containing GeoTIFFs
env.workspace = "Q:/Temp/Files"
#List all GeoTIFF datasets in workspace folder
fllst = arcpy.ListRasters("*", "TIF")
#Set the output path for batch file
txt_path = os.path.join(env.workspace, "geotiffbatch.fbt")
#Open batch file for writing
txt_file = open(txt_path, "w")
for fl in fllst:
#Construct path string to dataset
pth = os.path.join(env.workspace, fl)
#Construct string formatted for batch file
outStr = pth + ", x, 999, x, x, 1, x, IDF_GeoTIFF\n"
#Write string to batch file
#Close batch file
The batch file is ready to read in FRAGSTATS where you can then setup the metrics and output location. I would recommend looking at the tutorial package linked above for more information.
If the files were Ascii grids or other formats that FRAGSTATS will not automatically read the attributes of you could use
arcpy.Describe() to get the raster attributes necessary.