After reading tons of tutorials, looking up dozens of forums for 100% fix, I have finally found it.

This guide is tested in many different game settings and many different scenarios and so far everything working flawlesly.

Testing Environment:
Windows 8.1 Pro x64

If for some reason it is not working for you or it is working but you have different OS, please write in the comments section below.

Go to WinedD3D download page (http://savannah-nongnu-org.ip-connect.vn.ua/wined3d/) and download version 1.1.38 (24-Jun-2013 11:02)
Just download installer (file with .exe extension) and keep it still for now. No need to install it.

Go to 7-Zip website (http://www.7-zip.org/), then download it installer and install it.

Open installed 7-Zip archiver program and use it to navigate to folder where you keep your WinedD3D installer package. Find it, select it and extract it's contents. Extracted contents should contain 3 folders, named: $PLUGINSDIR, $SYSDIR and $WINDIR.

Locate $SYSDIR folder inside in previously extracted folder. Inside this folder you should look for these files: ddraw.dll, libwine.dll and wined3d.dll. Select these files and copy to your RT3 root directory. Usually your game should be in ...\Steam\SteamApps\common\Railroad Tycoon 3\.

After these steps you should be able to run RT3 without any problems. You can now use any setting provided in options menu, view videos and literally play the game. Well, except minor inconvienence. Notice how textures are pixelated and washed out? Well, we all gonna cover that next.

Go to Hawk & Badger Railroad webpage (http://hawkdawg.com/rrt/rrt3/rrt3.htm) and look for Blurry Texture Fix section, once you find it, download attached archive.

Simple as it is, just extract previously downloaded archive into you chosen directory. After done that, you should have a folder with two files, one of which should be named: d3d8.dll.

Now, it's just one last step, copy previously mentioned file, d3d8.dll, to RT3 root directory. Usually your game should be in ...\Steam\SteamApps\common\Railroad Tycoon 3\.

Well, you have your textured fixed, but another problem risen up. Video do not plays anymore, they just crash your game. Don't be sad, look to the next section.

If for some strange reason you do not want to have high quality textures and skipped 2nd step. You can skip this part of tutorial, since this part is only required if you applied both previously mentioned fixes.

Go to your RT3 install directory and look for RT3.exe file. Find it? Good.

Now, select or click one time on previoulsy mentioned RT3.exe file and then right click with your mouse. A menu should show up. Select last option from that menu, called "Properties". Now a window should pop up. Locate a tab called "Compatibility" and click on it one time. Window contents should change a little bit. Then, look for a section called "Settings" in it, locate option called "Reduced color mode", ant now mark the checkbox near it. After this, select box with selected default option with 8bit should appear. Change it to 16bit option. Finally click "Apply" button in the bottom to save selected changes and then "OK" button to close the window.