NOTE: Below is an updated version of my tutorial for TEW 2013. The tutorial was an adapted version of Judoku1819's (link) from the WMMA4 forums, so much love to him.
Due to some users having technical issue I've provided an alternative method that allows you to download a pre-created wrapper that I've made and uploaded ready to install. If you are new to wine it is recommended you use "Method 2".
What You'll Need
Method 1: Do It Yourself
Wineskin Winery (link) TEW 16 Setup .exe ("TEW2016_RETAIL.exe") TEW 16 Latest Patch .exe (optional - found in the tech support forum for TEW 2016, "TEW2016.exe")
Method 2: Pre-Made Wrapper (Easier)
Pre-Made Wrapper TEW 16 Setup .exe ("TEW2016_RETAIL.exe") TEW 16 Latest Patch .exe (optional - found in the tech support forum for TEW 2016, "TEW2016.exe")
NOTE: If using "Method 2" (the pre-made wrapper) skip to step 5.
Step 1
When you open Wineskin Winery you will need to install an engine and update the wrapper version.
To install the engine click the + button, next to the text "New Engine(s)" available, and chose the most recent one (the engine used for this tutorial is WS9Wine1.9.9).
To update the wrapper simply click update. (This may not be necessary)
Step 2
Hit the create new blank wrapper button and enter the name for the app. TEW 2016 is what I went with. This process will take a couple minutes and it is likely that you will be asked to install "Gecko" and "Mono". Hit yes and install these both as they are very important.
Step 3
Wineskin Winery will have opened up the location of the wrapper in finder. Open it up.
You'll see a screen with 4 buttons. Choose "Advanced".
Then choose the "Tools" button at the top of the page and hit "Winetricks".
Step 4
You'll need to run 5 winetricks and it is important you do these one by one. It is also important that you do not alter the install location of any of these.
NOTE: If this is not a fresh install of Wineskin Winery (i.e. if you've used it to create a wineskin wrapper before) hit the "Update Winetricks" button in the lower left corner
Firstly, search for "ie6". It is found under dll's. Select the tick box and hit run. Wineskin will display a message with a URL as well as opening a finder window. Download the file from the url and place it in the location that wineskin opened in finder. Once again search for "ie6", select the tick box and hit run. A window will come up if done correctly. Follow the prompts and install ie6. After installed it will prompt you to reboot but as we are just installing winetricks there is no need.
Secondly, search for "vb6run". Again it is under dll's. Select the tick box and hit run. This installation is quick and requires you to do nothing.
Thirdly, search for "jet40". Once again it is under dll's. Select the tick box and hit run. The installation is similar to ie6. Follow the provided link, download the file and place it into the finder window that Wineskin opened. After you've done this search for "jet40" again, select the tick box and run it. A window will pop up. Follow the prompts to install.
Fourthly, search for "native_oleaut32". This time it is under the "settings" drop down. Select the tick box and hit run. This is nice and simple and will complete by itself.
Finally, search for "allfonts". This time it'll be under fonts. It will take a minute or so but you don't need to do anything.
Once that has completed close winetricks and choose "configuration" from the top of the page.
Step 5
Now we get to the fun part. Open the wrapper and click the "Install Software" button and install TEW as normal. A prompt will come up asking you to chose the setup .exe. Select "TEW2016_RETAIL.exe".
When it has installed buy your elicense or copy it across from the computer that you have TEW installed. (I'm not sure on the copyright laws. I'm assuming this is fine, as you have already bought the game, but if not can a mod correct this. DON'T PIRATE, support the developer. I am also not 100% sure whether the DRM allows for the elisence to be copied as I purchased it through the new Mac app, so try at your own risk).
When this is done close Wineskin Winery and the new Mac TEW 2016 app if it is opened.
To navigate to the program files folder open a new finder window and click on the "GO" menu in the toolbar and choose computer. From there select "Macintosh HD" and the click on User>Applications (this is not the default applications folder). Select Wineskin and then Right-Click on TEW 2016 and chose "Show Package Content". Select the "Drive C" Alias (shortcut) and go into Program Files>GDS>TEW2013. I strongly recommend making an alias (shortcut) to this location as this is where mods/skins and patches are to be installed.
Step 6 (Optional)
Copy the latest TEW2016.exe that you may have downloaded earlier.
Navigate to the TEW2016 folder (see step 5 to work out how to find it).
Paste the file in here. A prompt will come up. To avoid bugs I recommend choosing "Keep Both Files".
Rename the original file "TEW2016_old.exe" or something similar. Rename the new file (that is called "TEW2016 copy.exe") to "TEW2016.exe".
And now you're done. Congrats. Enjoy TEW on Mac. If any problems arise feel free to reply and I'll do my best to help you.
Note:
To install mods navigate to the directory in step 5 and proceed as normal. One known issue is the ovsBooleanControl.ocx error AKA Runtime Error 339. This occurs when clicking on certain buttons. If this happens to you, navigate into User>Applications>Wineskin>TEW 2016 (Right click, show package content)>Drive C>Windows>System 32. Find the file named "OVSB~3IL.OCX" and rename it to "ovsBooleanControls.ocx". When the application is next started the "OVSB~3IL.OCX" file will be re-created but as we already have the correct file this is alright.
Proof:
http://i12.photobucket.com/albums/a210/alex_z9/Screen%20Shot%202016-05-11%20at%2010.40.36%20AM%20copy_zpsbthbtgb3.png
EDIT: For clarification this is confirmed working on both OS X Yosemite and OS X El Capitan, older operating systems should work but are not confirmed too by me. If anyone has any luck installing on OS X Mavericks or earlier let me know and I'll update this.