EqualX doesn't require MikTeX specifically. What the footnote says is
*Requirements. EqualX needs a TeX system to generate equations - specifically the programs pdflatex, gs and pdftocairo.
For Windows the recommended TeX distribution is MiKTeX.
Hence, the MikTeX requirement is misleading, it should also work fine with TeX Live. The fact that it also works for Linux supports this -- MikTeX only works for Windows.
A possible alternative: I hesitate to recommend LyX, even though it does what you ask.
LyX isn't really an editor in the normal sense, it is a graphical interface to some of the features provided by LaTeX and a selection of popular packages. Files are saved in LyX's own file format, but to generate PDFs, the LyX file is converted to LaTeX code in a temporary file, and pdflatex (or xelatex or lualatex) is run on the .tex file.
LyX does make it rather easy to make documents using the features that are supported in the GUI, but when you want to do something that is not supported, it can be more tedious than in a normal LaTeX document because the GUI can be more hindrance than help.
So some people like it, some people don't. It depends on what you want to achieve, how much control you want, and how much you dislike code.