I downloaded my normal windows gog version. Extracted its contents with innoextract, mounted the proper directory in DOSBOX. When trying to launch the game by "spire.bat" the game is being initialized, then suddenly DOSBOX just stops and ends.

The only message I came across is the following, which is left behind in the terminal where I started DOSBOX.

DOSBox version 0.74
Copyright 2002-2010 DOSBox Team, published under GNU GPL.
---
CONFIG:Loading primary settings from config file /home/kelda/.dosbox/dosbox-0.74.conf
MIXER:Got different values from SDL: freq 44100, blocksize 512
ALSA:Can't subscribe to MIDI port (65:0) nor (17:0)
MIDI:Opened device:none
DOSBox switched to max cycles, because of the setting: cycles=auto. If the game runs too fast try a fixed cycles amount in DOSBox's options.

Does anyone has a solution?

To answer my own question and for those seeking the same. :)

Like probably pointed out many times, just follow instructions on [url=http://www.uesp.net/wiki/General:Playing_DOS_Installments_under_DOSBox]http://www.uesp.net/wiki/General:Playing_DOS_Installments_under_DOSBox[/url].

Extract game with innoextract.
Install dosbox through apt-get
Change dosbox.conf (make backup first) through dosbox -editconf xdg-open
Make further changes according to uesp.net
And just make sure before running spire.bat run install.exe first, configure sound and video.

After that the game runs smoothly...