The only output format permitted by the ArcMap bookmark manager (v10.7) is an "ArcGIS place file (*.dat)" which is not entirely human-readable when opened in a text editor.
What is the file structure of an ArcGIS Place File? suggests it may not be possible to access content directly and probably requires ArcObjects to extract bookmark info.
Is there any other way to transfer bookmarks from ArcMap to QGIS?
Added 6-May 2021
Working from @PolyGeo's answer, here's some code that gets the info out of Arc:
import arcpy
srcPath = "D:\\SomeFolder\\Data\\"
srcFile = "MyMap.mxd"
# set working mxd
mxd = arcpy.mapping.MapDocument(srcPath+srcFile)
out_lst = []
# list frames within mxd
for df in arcpy.mapping.ListDataFrames(mxd,"*"):
for bkmk in arcpy.mapping.ListBookmarks(mxd, "", df):
e = bkmk.extent
out_lst.append([bkmk.name.encode("utf-8"), e.XMin,e.YMin,e.XMax,e.YMax,df.rotation,df.scale])
with open(srcPath + "file.txt", "w") as output:
output.write(str(out_lst))
Will jump into PyQGIS next.