How to Run MS-DOS Applications in Wine

There are a couple of things you can probably do to help:

1) Add the wineserver program to your startup applications, so that it starts when you log in, and is always running.

2) Run wine-preloader /path/to/yourgame.exe, so that wine adds some of its data to a preload cache.

I'm not sure how much, if at all, these will speed up the startup process for the game. I don't use wine much, but haven't noticed any particularly long startup times with it, beyond the first run (when it builds font caches and such).

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By the way, I see the issue you're talking about with the double-clicking. Just launch dosbox and run, or make sure your binary is inside of the .wine/drive_c if that's not the behaviour you want.
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You say dosbox is throwing an error when you run:
tachyonsos@tachyons-desktop:~$ wine '/home/tachyonsos/Desktop/TC.EXE'
Correct your sound settings. If that doesn't work, put it inside the ~/.wine/drive_c.

On my box, when I installed via software center it put a compiled binary in /usr/bin like this:

Configuration files are in ~/.dosbox. The wiki tells us how to configure the file and determine our midi parameters. To get those utilities we need sudo apt-get install pmidi.

Then we can see something like this:

So with gedit ~/.dosbox/dosbox-0.74.conf we can make this:

midiconfig=

look like this:

midiconfig=14:0

Which gives us this:

Next I added all the way at the end on the next line from where it says MOUNT lines here

mount C: /home/username/dosboxc  

Now when I double click an exe it tries to load in dosbox, as it should since I installed that last.

Now I make launchers for the EXEs I want to launch with wine to include the wine command and the URL.

You don't launch things in Dosbox with shortcuts. You load up dosbox and run them. At least that's what I do, and it works for me.

I definitely see no bug here.

Oh, and finally since I installed it anyway:

I needed to test that the sound was working anyway.