I had a look into this with elinks which I think is pretty much identical to links. I didn't find any option to print at all.
All I can suggest is to use the -dump switch and pipe to lpr or lp. I haven't tested at all but try something like:
links -dump -no-references http://www/domain.com/page.html
I've just looked at keybindings and realize that I have a bind set up to print.
In Setup - Document - URI passing I have a 'print' option like so 'printhtml %c'
printhtml is basically a script (in my PATH) that does as above:
elinks -no-references -dump "$@" | lp 2>/dev/null 1>&2
Then put in the keybind options the key combo to use for URI passing.
You can have more than one URI passing options setup - I have one for print and one for print with references.