It is generally better to use Linux dosbox rather than Windows dosbox under wine, unless it's a game like Eye of the Beholder, where Windows-specific extensions to dosbox are used (and even then, I just live without the extensions). Your distro probably has an adequate version of dosbox for this game.
Generic DOSBOX installation:
1) Extract the game. I usually use the Windows installer under wine for consistency, but you can also just use innoextract
. Note that even if your distro supplies innoextract, it may not be recent enough to support gog's version of Inno Setup. Extract with "innoextract -g -e setup_....exe" and the game will be in app/.
2) Delete the Windows dosbox: rm -rf DOSBOX
3) Create workable dosbox.conf files out of the gog-supplied files. Generally there is a dosbox<game>.conf and a dosbox<game>_single.conf. For network games, like Syndicate Plus, there may also be a *client.conf and *server.conf. There may be others for extra support, like *setup.conf. The dosbox<game>.conf contains most of the dosbox configuration. I normally use my own tuned dosbox config and just "diff -wub" with the supplied config to determine if there are any important changes; in that case, I copy those changes (and only those changes) into all of my game-specific configs. The main issue you need to deal with with the game-specific (single/client/server/etc) configs is that it's run relative to the DOSBOX dir in Windows, so convert ".." to "."; if CD data is used it might also be necessary to edit the CD descriptor files and change the mount command a bit (since it's case-sensitive, for one). As I said, I also tack on any relevant config changes from the main one.
In short, replace .. with . in *client.conf and *server.conf, and just use dosbox's default config for the rest.
4) Run dosbox using the created config file(s). If you want to use your own config, as I do, run "dosbox -userconf -conf <gameconfig>.conf". Here, gameconfig is your translation of the *client.conf or *server.conf file. If you want to use an edited version of the supplied base config file, just replace -userconf with "-conf dosbox<game>.conf" or whatever. Note that you can create/overwrite the default config by starting dosbox and using "config -wc" or "config -wc file". The former is unsafe if you don't want to accidentally overwrite your main config, though.
I personally do a lot more than what I described here, but only insane idiots would want that. For example, I use unionfs to allow me to keep the game data read-only and pristine, and I use wrapper scripts to simplify everything for me. I also enable munt where possible, and have my dosbox compiled for glide support (e.g. Redguards or Tomb Raider). Neither of these appear to be needed for Syndicate Plus, though.
I have never used networking in dosbox, so I can't help there if it doesn't work out of the box for you.
Edit: while I had no intention to provide info on how to make a desktop file/icon-based launcher, I should at least mention that you can convert the icon file (usually either gfw_high.ico or goggame-*.ico) using imagemagick's convert; e.g. "convert goggame-1207658992.ico goggame-1207658992.png". You will end up with more than one png file; pick the best one using an image viewer or whatever (my install script automatically picks the 256x256-RGBA one using "file").
Edit 2: In my attempt to finally update all of my Windows games, I noticed that games with cloud save support also mount another directory that obviously isn't necessary for Linux. I didn't even realize that dosbox had built-in overlay support, but I will continue to use overlayfs for myself.