In DOSBox 0.74, I can run GWBASIC.EXE without any problem (DOSBox reports 632 KB of free conventional memory). It is GW-BASIC's version 3.10 dated 01-07-1989 with filesize 72576 bytes. On screen it shows:
GW-BASIC 3.10
(C) Copyright Microsoft 1983,198661934 Bytes free
Whenever I try to launch the program in one true DOS 6.20, so without the use of any emulator, I receive an "Out of memory" message and the DOS prompt reappears instantly.
I have reduced the setup of that DOS system to the bare minimum, and currently I have 589552 bytes of free conventional memory as reported by the MEM command. To me 575 KB seems like an insane memory requirement. I think in the past I could run GW-BASIC in DOS 3.3 on an XT computer (8088) that had only 512KB of conventional memory.
So what is the minimum memory requirement for GW-BASIC? Or broader, what are the system requirements to run GW-BASIC, in case that "Out of memory" message is to be taken as a generic, but silly error message?
[Further steps]
Raffzahn's point about requiring 'at least 1 floppy drive' looked promising to me. I quickly attached an USB floppy drive and witnessed the Equipment Status change from 0026h to 0027h which means BIOS recognized the floppy drive. Sadly, it did not help in launching GW-BASIC.
Next I dug out an old Pentium 166MHz and there launching GW-BASIC worked flawlessly. Following this, I tried to mimic the Pentium's DOS setup on the current system (Intel Pentium 1.73 GHz dual core processor T2080) but found it wasn't the cure I was looking for.
[Conclusion]
My real intrest in GW-BASIC was to study how the PLAY statement operates and what differences there might be between GW-BASIC and QBASIC in this respect. Since by now I have taken the trouble of setting up the old Pentium, I can already do all the testing that I need. So I won't pursue this on the newer computer, where it's probably the more advanced hardware that causes the problem. Next quote from paxdiablo's answer rouds it up:
I suppose the bottom line there is that it's not that the memory requirements are an issue, but that the ability to run it at all (at least in a supported manner) is the problem.