Thank you for your post.
I am unable to replicate the issue. I have installed FileMaker Pro 16 Advanced (64-bit) on my Windows 7 machine and made Chrome Version 58 my default web browser. Without any applications open, I launch FileMaker Pro 16 Advanced, and when I get to the Launch Center, I press F1, Chrome launches and presents me with Help.
After closing Chrome, I also pull down the Help menu and select FileMaker Pro Help. Again, Chrome launches and presents me with the Help page.
Let me know what I am doing differently than you so I can replicate the issue.
Sigh. I'm not sure what the answer is. I cleared cookies and cache and disabled all extensions, but still had the problem. Works fine with FM15, as well as with external links from my email app, etc.
I even just went as far as upgrading to a beta build: Version 61.0.3116.0 (Official Build) canary (64-bit), which gets added as a second install that is separate from the original Chrome 58. But I have the same FM16 issues there even with a fresh install.