It looks like elinks is available in Homebrew[1], so the only added step is brew install elinks

[1]: https://github.com/mxcl/homebrew

Not guaranteed to not break: curl -s http://randomfunfacts.com | grep "<td border" | sed 's/<[^>]*>//g' | sed 's/&nbsp;//'

It does work on OSX, you just need to install elinks (brew install elinks ?)

Related question: How would one write this without the elinks dependency, using curl or wget?

You need elinks, that's all. So: brew install elinks