There is no need to convert the maze to mesh. Select all curves and hit Ctrl-J to join them together.
In the curve settings make sure it is set to “2D” (which will remove the chaos seen in your second screenshot) and then use the curve extrude tool:
If you want the walls to have thickness (and not just height), I think this might easiest be done in the vector graphics program of your choice. In mine (Xara Designer Pro) I import the SVG, join the curves together, increase the line thickness, convert line to shape and export the now thickened walls again as SVG (Sounds complicated, but is done in a few seconds. I’m pretty sure there’s something similar in Inkscape…):
And look at those beautiful bevels! All for free if you keep this curves.
BTW, mazegenerator.com does not exist, the domain is mazegenerator.net…