Does there exist open source LaTeX converters that produce Markdown, in the same manner tools like latex2html does?
Pandoc is what you need. This tool helps you convert any markup format to another one including from latex to markdown.
For your need, first you need to install pandoc into your system (available for all MacOS, Windows, Linux) and then use this command line
pandoc -s example4.tex -o example5.text
You can also convert your texts online by using a tool provided here.
This project, https://github.com/loopspace/latex-to-internet, provides a class which produces text output in a variety of different formats. It comes with a huge number of caveats, but it does work.
The underlying principle is that "The only thing that understands TeX is TeX itself" so it uses TeX to parse the document and produce the desired output.