What you get: a regular DOS HOMM1, which is launched via DosBox just after mounting the attached ISO image of the disk. Everything is archived into the Win32 binary installer.

1. Install the game by running the installer, using Wine or via PlayonLinux. Do not click Run, but exit after installation.

2. Move all files to your Dosbox directory. Its better to use DosBox wrapper (DBGL or similar).

3. The Dosbox configuration in order to run can be found in file "dosboxHOMM1.conf". Its pretty generic, but you need IPX for network abilities.

4. To run, you need to mount the CD image "homm1.gog" (its ISO 9660 iso image), enable IPX(fully optional, required only for networking) and start the game. Exact lines are seen in "dosboxHOMM1_single.conf" and similar files. You can either add it to your existing Dosbox configuration or enter manually.

Thats all.

Requirements:
- Wine /and PlayOnLinux(option)
- DosBox /and DBGL(option)

You can avoid the call to WINE/PoL by using innoextract, a CLI tool.
See here for more details:
Install the HoMM series on Debian/Ubuntu/Mint/etc.

Any question welcome of course ;)

The structure of the files seems to be changed.
1. There's no longer "dosboxHOMM1_single.conf" or anything like that (however there's still DosBox folder in GOG installation).
2. Trying to launch Heroes.exe results with "The program cannot be run in DOS mode.

I'm a bit confused...

I guess, you use polska distribution of the game. For the unknown reason GOG provides Windows version for this language.
Either use Wine to run this Heroes or reinstall from English distribution to make recommendations from the current topic usable.

Well, wasn't sure it's Windows exe, because there are still DosBox files in installation folder, but it may be caused by some GOG generic packaging procedures, indeed. But still – running Heroes.exe with Wine causes some "32-bit" errors (Unhandled exception: privileged instruction in 32-bit code (0x0042173d).) and the game does not launch.

It was important to me tu use Polish version because I wanted to play with my kids :) but it's good to know that for my own purposes the game may still be playable under DosBox in original. Thanks!

Why use the inferior DOS version? It's inferior - it doesn't have a map editor!

Use the Win95 version!!
Just install Win 98 on VMWare player! Geez, not that hard