you should really try the cvs version of dosbox
there have been quite some improvements in the exception generating code.
http://cvscompile.aep-emu.de/dosbox.htm
this one for example

Yes, try the CVS. DOSBox 0.62 is ancient - the latest official release is 0.63, but lots has changed in the CVS since then.

Thank you two for your fast answers.

I downloaded DOSbox 0.63 and the cvs. Thank you for that information.
The game still does not start however. The error message is the same as before.

If you should know any other solution for my problem, please tell me.

Since I have no idea how DOSbox and the game work I don't understand why it reports memory problems. Maybe you could tell me possible reasons. I could then search for a solution myself (once more).

For your information: From the game's readme file

RAM Advanced Tactical Fighters requires 8 Mbytes to run. The exact memory requirements are as follows: […]
Show full quote

RAM
Advanced Tactical Fighters requires 8 Mbytes to run. The exact memory
requirements are as follows:

CONVENTIONAL
You must have 490Kb of conventional memory free to run U.S.
Advanced Tactical Fighters.

XMS
You must have 6,900Kb of XMS free to run Advanced Tactical Fighters.

If You Are Getting Error Messages
If you are receiving an error message when running the game, you can
generally solve the problem by making a boot disk. Please refer to
the 'CREATING AN MS-DOS BOOT DISK' section of the INSTALL GUIDE for
detailed instructions.

Can you type MEM > mem.txt in DOSBox and then post the contents of mem.txt?

Sure, here it is:

637 Kb free conventional memory
15296 Kb free extended memory
15296 Kb free expanded memory

Does the rip need some cd thing like fakeCD or so?

Concerning memory, set ems=false in dosbox.conf as
the game seems to require xms only. Also try xms=false
in addition to see if it can handle memory itself
(you could use different values for memsize inside
dosbox.conf, like memsize=8 or memsize=64).
And maybe loadfix helps (allocates some low dos mem).

If if doesn't help, you could test the following:
change the core (dosbox.conf: core=dynamic or =full)
change the cycles (cycles=500 for testing)
rename the game directory (be creative with this point 😉
configure the game different (like disabling soundblaster etc.)

hth

Thank you, WD.

The game does not require any additional program like fakeCD.

I tried disabling ems without a result.
Disabling both ems and xms caused the game to run however.
(I guess - as you wrote it - that memory is now provided as requested.)

Not only do the setup and menu now load, even the flight simulation is playable.
Everything still is very slow (up to one minute loading time between two screens in the menu). I am now going to figure out the best configuration.
I will post the result here for people that experience the same problem as I did.

Thank you all for your help, guys!