No, your browser never sees any of the vector stuff.
However, for your needs you should be able to print it with good quality anyway, just don't do it via a screenshot (well in theory it could work well too),
In your browser when on that page, use the print dialogue in the browser and print it to a PDF or directly to a printer. For example with Chrome's own print dialogue (notice the advanced settings too) you will get some pretty good settings and choices and it is using the the best underlying quality for printing directly, not doing it manually via a screenshot. Use 600dpi or 1200dpi, choose a big paper size if you would like that etc.
Take notice of the actual printed area and paper orientation (portrait/landscape).
So for short, no, no vectors, but good end result anyway?