You still have to trace that to convert the lines to vectors (it’s a function in Inkscape, not meaning manually trace it). Just saving a raster out in different formats doesn’t convert it to a vector - and only vectors can be cut or scored on laser cutter.
From your image - I’d go back to the source and see if there’s a vector version available to download (not JPG or PNG). There usually are or maybe you could get a new map of the area with this tool:
https://community.glowforge.com/t/cartocuts-topographic-maps-for-makers/