I've taken a brief look at the source code. The HTML parsing and rendering code is a core part of elinks, and while it appears to be somewhat modular, it is not a separate library. It might be possible to separate it, but not without a good deal of work.
If you're curious, the src/README file provides an overview of how the various parts depend on each other. The HTML parsing and rendering code is under src/document/, but also depends on src/viewer/, src/config/, and other parts of the code.
But to start, see if you can get elinks -dump to do what you want. Good UNIX tools are designed to work together with other tools, and this is how elinks provides its rendering service without being an interactive browser. You will probably want to use a custom config file to control how you want the dump to look. Take a look at man 5 elinks.conf, in the document.dump section... and of course man elinks to read up on the -dump and -config-file options.