IINM, the sub boxes in the referenced thread are finished in Formica brand plastic laminate (specifically #909 black in gloss finish)
There are at least half a dozen mainstream domestic and even more custom European brands of plastic laminates available, but most of the DIY or home handyman big box stores won't likely carry in stock, and yes shipping can be expensive (even though the box is mostly full of air).
Try searching location kitchen cabinet/countertop shops - note that there are 3 standard domestic sizes (30x144in, 48x96in and 60x144in), and while the countertop shops may not always stock what you're looking for, if they're willing to sell retail, and you're willing to wait, you can often pay a lower landed net price than by ordering from out of town. Plus they'll generally have much better terms with vendors and shippers for remediation of shipping damage, which definitely happens frequently.
As for fabricating with plastic laminates, in addition to the 3 sheet sizes, there are several thickness grades - one of which is specifically intended for radius wrapping of edges. Generically referred to in the trade as "post-forming" grade, it's very fragile, but can be fabricated to as small as a 3/4" full-wrap (i.e. 180 degree) radius, with specialized machinery using controlled heat to temporarily soften the material. It takes a fair degree of practice to post-form wrap it with hand held tools, and unlike thermo-formed foils (which also require specialized production facilities) cannot be radiused in two directions.
The substrate core of HPL ( High Pressure Laminates) consists of layers of resin (generally phenolic) impregnated paper (general kraft), and will usually reveal a medium to dark brown seam on exposed finished edges. Felt markers reasonably closely matched to the predominant face color can generally disguise this edge, but will not have durability of the p-lam itself.
