vectorising is basically going into Coreldraw / Illustrator and drawing in all the lines, curves, and designating the lines a thickness and the fill in between certain encased lines / shapes with a colour. Then when you have these shapes you can layer them to replicate the finished work of art / design which in this case is your playfield design.
That's OK for a print file but not for a cutting file. You can designate a line width but when it comes to cutting all you get is a hairline in the centre. For a cutting file you have to hand draw both sides of the line
Illustrator allows you to outline a line/stroke path. ie Object/Path/Outline stroke. The would give your cutting path along both sides of a designated line.... possibly? Don't know if that would help in a cutting file procedure though .. as Im not ofay with this side of things. FYI in anycase.
Im not familiar with Illustrator... all my vectoring is done with Corel