Hi,
None of my testing with a mouse went well at all so I don't even use it. I was going to disable it completely but I thought people might get upset so I left it in as an option but it's really not the way the game is meant to be played unfortunately. You should be able to use arrow keys to move and then CTRL to shoot and space to open doors - that's how the game was designed. I also find when I play Wolfenstein 3D (which was created in a version of this engine I'm using) I often have trouble with the mouse so it may just be a limitation of 1993 technology, I'm not sure. I don't remember ever being able to strafe in the old Wolfenstein but I could be mis-remembering.
If you download the newest version (v2) that's available now, you should be able to turn left and right much faster than in version 1 which should hopefully eleviate your need for the mouse altogether (I assume you want to be able to turn around quicker). I sped up the ability to turn in the new version quite a bit and we can turn it up even faster than it is right now if we need to. I was getting frustrated with not being able to turn around to face enemies quickly so I sped up the turning rate.
I'll do some more testing with a mouse and if I can somehow get it working properly, I'll be happy to change the controls to be more in line with modern shooters but I can't promise anything. I did already try it once and it didn't go well but I can try again in the newer engine. When I previously tried to get the mouse working I was in v4.62 of the engine and I'm on v5 now so it might work better now, I'm not sure. If I can figure it out, I'll make some changes to the demo and post an update.
Thanks for playing btw, I was just trying to make a weird little fan game. I don't think anything based on a Lynch property would work if it wasn't a little weird right lol?