Here is an easy Tomb Raider II fix for Windows borders showing during videos and gameplay when the game is fullscreen. It requires the use of a 3dfx Glide wrapper. This works for the retail CD version of the game. I am (so far) unable to get it working for the GoG version. It should work for Windows versions XP - 8.1. I'm not sure about Windows 10 since I don't have/use it.:

1] Let's start with a fresh Tomb Raider II install. Back up any saved game files. Uninstall any mods and Tomb Raider II. Delete the Tomb Raider II folder. Reinstall Tomb Raider II and your saved game files.

2] Method 1 [for regular computer users]: Do a Google search for nglide made by Zeus Software. Install nglide using an administrator user account not a standard user account.

Method 2 [for advanced computer users]: If you prefer open source options, search for the term "openglide" using your Web search engine of choice. A link to Sourceforge should come up with fbarros, glidos, and swstiletto as the authors of the project. Download the most recent binaries of OpenGLide, or tweak and compile the source code to your liking. Copy Glide2x.dll and OpenGLid.INI into the SysWOW64 folder.

3] Reboot your machine.

4] Open the Setup Tomb Raider II link in your Start menu.

5] Click the "Use Defaults (may not be optimal)" button, and then click the "OK" button.

6] Start Tomb Raider II. If all seems to be working fine, close out of Tomb Raider II. Go back to the Tomb Raider II setup program and adjust the full screen resolution to your liking.

7] Enjoy!

My computer specs:

Windows 8.1
Intel i7-2600
Nvidia GeForce GTX 770
All drivers up to date

You can try and patch the tomb2.exe with an hexeditor in the following way: at address 0x045F84, replace CF00 by 0080, and (optionally) at address 0x045F92 replace 0004 by 0000. This will change the parameter of the call of CreateWindowExA to use the popup window style (and extended style to zero).
The downside of this solution is that also in windowed mode there will be no window borders.