Can I bundle the Visual Studio 2015 C++ Redistributable DLL's with my application?

There are 4 files in C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC\redist\x64\Microsoft.VC140.CRT. Does that mean I just need to copy them to my application's directory during the install process?

Yes, and the paragraph you quoted means just that.

Is this OK to do? Do I need to show a license? Why aren't more people doing this instead of requiring yet another preinstall of the redistributable?

Technically, that's OK to do. If you want to be pedantic about it, you may include a note in the readme or help/about to the effect that VC++ 2015 redistributables provided in "local deployment" mode as explicitly allowed by Microsoft's Deployment in Visual C++ (with more links to the file lists and licenses at Redistributing Visual C++ Files).

As to why more people don't do it, I'd guess that (among those who care at all):

• for a single module app like MyApp.exe it's easier to build it with everything linked statically as to eliminate external dependencies to begin with;
• not including those files saves 1+ MB from the distribution (presumably download) size;
• running with private copies of the runtime ("local deployment") shifts the responsibility of updates to the maintainer, so that in case of a critical/security fix the package would have to be reissued timely - as opposed to "central deployment" where it would likely be delivered via Windows Update, with both the good and bad that may bring.

If you have problems with the prerequisites installer you also have the option to install the redistributables as merge modules. As the same MSDN article mentions:

Another option is to use redistributable merge modules (.msm files), which can be found in Program Files [(x86)]\Common Files\Merge Modules.

Using merge modules it is a much cleaner option than manually adding the files. The files can be deleted accidentally by another colleague which does not know why they are there, or one of them might not get installed, etc...

All editions of Advanced Installer have support to include merge modules, including the free edition.

• how to add a merge module into an Advanced Installer project/package