UPDATE April 2019:
It was brought to my attention that Decoframe 2, 3 and 4 all had multiple pieces in them - sorry about that! That's what happens when you flip stuff in Cura and try to export it :p I have now uploaded fixed files where one file is only one corner. Sorry for any grief this caused.

Furthermore, after reflecting on the checkered board part, I have a few notes.
First of all, the caps fit into the slots perfectly - theoretically speaking. However, at least in PLA the tension of the perfect click and hold fit of the caps will eventually put tension on the entire board and by the end make it difficult to get the caps in. This means that you need to either plan where you put caps to get even tension while working(unlike end to end like I did), or you can scale down the caps ever so slightly(maybe 99% or 99.5%?) to just take a little bit of the tension off. This is untested as my board is done and looks ok. If you do scale down, I'd love to hear how that went and if you needed to use glue to keep the caps in :D

THE DECORATIVE FRAME has now been printed! :) Everything fits absolutely perfectly. And without patting myself too much on the back, it looks great!

There is an issue with the actual chess board itself though - if you print it as is in PLA, there is a very real risk that the corners will start to curl downwards when you put the caps on because it's so thin and the tension pulls on it. You need to make a choice how to deal with that.

1: I made the decorative frames with an empty middle to save quite a lot of filament, but if you add material to that middle again so it has a full, flat surface you can then glue the slot board onto, that should keep it flat even with tension from the caps. This is untested though.
2: Glue the slot board onto a flat surface you KNOW won't warp from a little tension - glass, metal or a hard wooden plate. Just make it slightly smaller than the board so it can still fit into the frame, and not too thick or the plate will rise above the frame
3: Start from the middle and work your way out, with a bit of violence, if you finish the whole board in one sitting, you can still make your caps fit in there and have them stay there. When you press the board into the frame, the warp isn't that visible so you can live with it this way

I'm currently contemplating a change to the caps to make them a little more sturdy and easier to force into a warping board so option 3 is more viable. But I absolutely suggest the fixating plate below the board as that's the simplest and then the caps will fit perfectly :)

Edit 1: The cap was a tiny bit too large. The new version is a perfect fit - sorry if anyone printed the faulty ones.
Edit 2: I am currently printing this for myself. The chess board by nature is very thin at the bottom, so if you use PLA, it is prone to warping AFTER the print because it's so thin. To combat this, glue it to a wooden board or something else flat that won't warp easily. Alternatively you can add a platform in the middle of the decorative frame or you can make the bottom of the board quite a lot thicker
Edit 3: Added pictures of the finished print :) Also added a warning about the actual board and how to address the challenges that comes with tension and PLA

This is a chess board with an optional dragon cliff decoration. The board is made with room for small magnets. Just put a magnet in the cap, glue the cap in the board and then you can put magnetic chess pieces on the board and it'll be dragged to the center of the square. If you use magnets in the slots AND magnets in the chess pieces, make sure all the magnets are turned the same way in all caps and that the reverse pole faces down on all your chess pieces. Otherwise the magnets will repel each other in some places, and that's not the point of this(although an excellent gag gift for a chess lover :p)

Design credits:
Board with magnetic slots: Me
Dragon heads: Shira's dragon door knocker(https://www.thingiverse.com/thing:1458545)
Rocks: Terrain4Print's rock formations(https://www.thingiverse.com/thing:2571112)
Meshmixing the whole thing together: Me

The magnetic chess board with the caps can be used for any purpose you please. The decorative frame follows the licenses from the original authors