It's pretty simple, really: Microsoft adopted TNR as a default system font in Windows in 1992. Windows achieved remarkable dominance — it still holds more than a 90% share of the desktop OS market — and Microsoft Office achieved similar success in the productivity software market.

So essentially, Times New Roman became a ubiquitous standard simply because it was the default font on the word processor used by the majority of the world — long after it was no longer used by the newspaper which commissioned the font and after which it was named.