Am I seeing the picture wrong? It looks like the holes are cut with the grain and the sides are pin nailed (and glued) onto the end grain. The ends have CR Onsrud inverted pin router with a spiral bit written all over them. The grooves, maybe a magic moulder custom ground profile to a little over half the hole? Or a whiteside core box bit?
Of course the easy thing would be to hire this out, if there is someone available. If I were setting up in the business of making doo dads like this, I would buy the biggest cr onsrud pin router I could get my hands on. These come up used, sometimes for penny's on the dollar, and the big ones can put more hp into a spindle for the least amount of money of any machine I can think of.
https://www.youtube.com/watch?v=TI18ZWaG1_c