I have the same problem in tons of games, why was walking with the mouse so standard
Two solutions for two different platforms.
1.) Dosbox based games: Novert.com
Simple dos based program that will disable any Y-Axis input from your mouse (no vertical mouse movement)
Add "Novert.com" in your autoexec part of your .conf file
2.) Windows based games: XMBC (XMouse Button Control)
A neat little mouse injector for windows based systems that allows for added mouse functionality.
The program will only effect your mouse when the program is active.
What we want it to is to lock the Y Axis, so windows will no longer accept any vertical mouse input at all.
(Settings -> Hotkeys -> Other Hotkeys) Tick "Enable global hotkeys" -> Set "Toggle Y Axis Lock" -> OK -> Apply -> Close
In this case, you want to use XMBC.
Word of warning, this will not "fix" everything mouse control wise with this game.
You will figure out that strafing in older games around this era, was done by applying a strafe modifyer together with a turn key, this means it will also apply to your mouse movements.
TL:DR - Even with this fix, you will not be able to turn & strafe at the same time.
*The issue with turn & strafe at the same time, is something that cannot be corrected from outside of the source-code to the program it self.
Only way it would ever see a change, would be if someone has the source-code to the game or reverse engineered it to such a degree that actual strafe key support could be added (this is possible to do, easy with the source code, quite difficult without and has allready been done in games such as Wolfenstein3D though eighter the SDL source engine or the ECWolf engine)