Can I download and safely install and use a debugger on my host computer?

You are fine to install debugging software on your host machine.

The disclaimer is a fairly generic disclaimer about experimenting with viruses and malware; keep that stuff in a digital cage or else risk infection and a damaged system.

The disclaimer on that blog post as follows:

“Disclaimer: Do not attempt to analyze malware without first setting up a secure, virtualized environment. x64dbg should not be installed on your host machine to analyze malware.”

The key point here is unless you plan on analyzing malware, installing x64dbg on your host machine is fine. But if you are planning on analyzing viruses and malware, the best practice is to do that on an isolated — and easily disposable — environment.

The disclaimer about malware is fairly generic: If somehow you have a known bit of malware and want to see how it works, you are best off setting up a virtual machine so it can be nuked. Either nuked if something goes awry. Or nuked after you do what you have to with the malware and just need to dispose of it.

I mean technically speaking you can install a debugger on your main host machine and analyze malware that way… But then what happens if the malware does its job and infects your system? And if nothing goes wrong how do you even know nothing has gone wrong? Will you feel safe using your main machine after having known malware on it? I wouldn’t!

Virtual machines are relatively simple to set up and easy to dispose of as well. If tour whole system gets infected, what are your next steps past rebuilding your system from scratch? Who really wants to do that?

And to put this all in clearer context, that blog post seems to be focused on using x64dbg specifically for malware analysis as it states in the first paragraph:

“x64dbg is an open-source debugger for Windows that is a popular malware analysis tool. A debugger is used to step through code as it executes, so you can see exactly what it’s doing. Debuggers are essential for troubleshooting bugs, but they’re also used to reverse engineer malware.”

So unless you are engaging in malware analysis, none of those disclaimers apply to you.

If you intend to download malware, set up a Host Only virtual machine, temporarily connect it to the internet, download the malware here. Then disconnect from Internet.

Do not use your host machine, lest it becomes infected and needs to be rebuilt.

That is what they mean "Use a secure environment"