Cool dragon.
This is a very complicated project - not so much because of the number of pieces (although that’s going to be challenging also) but because the fit must be precise. The creator has planned for a specific but unidentified amount of laser kerf in sizing the pieces.
You will probably have to experiment to get things to fit. Be aware that plastic that is nomenclatured as 1/8 inch may or may not measure 1/8 inch. Different colors may also be very slightly different thicknesses. IDK if you can buy 3mm plastic … but it’s my experience that so-called 1/8" acrylic is a little thin so it may actually be closer to 3mm.
Here are some specific thoughts for you:
1. Artwork
You need the svg file. The others appear to be various rendering, etc. files. First you have to open the artwork (svg files) and make sure all the vector outlines are 0.001". When I open the file in Illustrator it thinks the vectors are 0.0139" which will cause it to want to engrave and not vector cut. You can make this change in Inkscape or Adobe Ilustrator.
2. Plan to cut in smaller batches
The svg file is sized for a sheet that’s 45" x 30.1". I think you will have poor results if you try to cut everything on that sheet in one batch. You will find that the laser bed(s) are not perfectly level and the settings in the rear LH corner can be quite different than the settings in the front RH corner of the bed. You could cut it all from one sheet using multiple cuts, but edit the artwork to separate the pieces into separate batches (using different vector colors) and then refocus for each local cut.
3. Buy your plastic.
IMO, best place to get acrylic is Allied Plastic on Shady Trail. They carry just about every color possible and they’ll sell you as much or as little as you want (i.e., you don’t need a full sheet).
4. Experiment on the plastic that you bought.
(a) Cut two small pieces that are intended to interlock, trying a couple different power/speed settings. See if they actually fit together.
(b) If they do … you’re golden. Lay out your pieces into however many colors/sheets you want using the svg file. Break into smaller local batches like I described above. Be forewarned that as the laser lens gets dirty the settings can change over time so you want to be cutting as close (temporally) to your experimenting.
(c) If they don’t fit … you’re going to have to modify all the pieces to make them fit - or plan to file a lot of tabs/slots. Adobe Illustrator and CorelDraw can both use either svg or dxf files (dragon base only), but be forewarned that dxf files tend to have disconnected segments. I’m most familiar with Illustrator, which has a function where you can offset an existing vector path without redrawing the vector. CorelDraw has something equivalent but IIRC it’s a little more kludgy.