I searched all of Microsoft Support's website, it showed quite relevant results but none of the articles are for Windows 8. And by following steps used in the Microsoft articles, I'm afraid this will cause problems to my computer.

Yes, even if I put my filename as "userChrome.css", it's still considered a text (.txt) document.

Since it's getting late, I will post my next reply tomorrow.

Try to create a new CSS document userChrome.css and be sure to have "All files" selected when saving the file and not Text files.

You can also try to rename the file with enclosed quotes "userChrome.css" to force .css file extension.
Windows can be quite stubborn to keep the .txt file extension.

Jscher2000 suggested Create New Text Document, therefore making userChrome.css a text document. When saving, I don't see "All files" option.

Here is how I make the userChrome.css file:

Help - Troubleshooting Information - Show Folder - create chrome folder - right click new - text document, name it userChrome.css - paste in all content to remove throbber, it still exists.

When you create a text document then you get a (hidden) .txt file extension and not .css, so such a file won't work.

You can either use the text editor to create a new file and save this files as userChrome.css or try to rename the file with quotes around the name in case the .txt file extension is hidden.
The Save as dialog should have a selection choice to show All files instead of Text files.
Choosing all files will prevent getting the .txt file extension.

Ok, I recreated userChrome.css, rightclicking and selecting new text document, pasted

@namespace url(http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul);
.tab-throbber { display: none !important }

into file,

saved as all files, but I'm afraid this will damage my computer.

Microsoft won't allow quotation marks around userChrome.css .

Does the file now show as a CSS file and no longer as a text file if you check the properties in Windows Explorer?

All files only means that you do not filter the file window to only show files with a .txt file extension, but it shows all files is a folder.
As long as you do note replace (overwrite) an existing file then nothing will go wrong.
But if there is already an existing userChrome.css file in the chrome folder created by the ChromEdit Plus extension then you can replace this file with the new file.

What really is Windows Explorer?

It still shows a text document.

Maybe use Firefox to create and save the text document if you aren't able to do this in Windows.

You can open the Scratchpad (Firefox/Tools > Web Developer;Shift+F4) and paste the text in the editor window.
Save the file as userChrome.css in the chrome folder.

Windows Explorer is the program used to show folder contents in Windows. It is the program that opened when you used the "Show Folder" button.

You could download the following file to your computer, then edit the file name to delete the -tab-throbber part. Because you are hiding the .css file extension, I think then the file will show as being named userChrome with a file type of CSS file (or similar) and you can move it into your chrome folder.

https://jeffersonscher.com/res/userChrome-tab-throbber.css

(right-click link > Save Link as)

Oh, thank you, Jscher2000!!! There are no more throbbers appearing on the left side of the tabs. THANKS A LOT!!!!!!