Laser-cut items generally need "ties" or "nicks" to keep the final piece attached to the original slug until punched out by the player. You add these by leaving tiny gaps in the cutline of your SVG file.
There are paid tools like The Game Crafter's Component Studio that can add "nicks" easily. However, if you'd like to accomplish this for free with a little extra work, here are the steps for doing it in Inkscape.
Step 1: Make a rectangle exactly as wide as the intended nick. For 6mm acrylic, that's 0.005". Make it long enough that you can grab it easily. The rectangle must have a solid fill and NO stroke/border.
Step 2: Put copies of your rectangle everywhere you want nicks to appear. It has to be normal/perpendicular to the piece's contour, so it's easiest to do on vertical or horizontal areas.
Step 3: After ensuring that the rectangles are in front of your piece, use the Path -> Union menu command. Your little rectangles turn into studs on the original piece.
Step 4: Zoom in. A lot. Here I'm using 4000%. That's not a typo.
Step 5: Select the two vertices at the tip of the stud.
Step 6: Click on the "-" icon indicated by the arrow.
Step 7: The vertices vanish, leaving a single curved segment.
Step 8: Select the curved segment, then click the "remove segment" icon indicated by the arrow.
Step 9: A glorious little nick. The laser will skip over this while cutting.
Step 10: Repeat for the other studs.
I actually saw that tool for optimizing the cut path, completely missed that it could add nicks as well! Very useful, and you can see all the work it’s saving you :)
Edit: So the command is "Split at point" and lets you give a nick size in inches (or whatever you choose). However, it splits it at some point that you click with the mouse. The method I showed above lets you be precise with the location by aligning the rectangle with other stuff in the file.
If precision isn't important, the "Split at point" is the way to go.