The classic Nintendo Cabinets, like donkey kong, dk jr., popeye, etc. were made in Japan and the U.S. simultaniously. The only exception that I know of is that, iintially DK was Japan only, but they eventually started making Donkey Kong cabinets in the U.S. too.
The Japanese-made cabinets are plywood and have that hard enamel like coating on them.
The U.S.-made cabinets are particle board and don't have the coating, they're just painted.
With a game like Popeye, the fact that it's ply just means that it was made in Japan, it doesn't tell you much about the time it was made (early vs. late). This is because, by the time Popeye came out they were making Nintendo cabinets in both Japan and the U.S.
As for the DK boardsets. Nintendo used 4-board stacks in the early japanese Donkey Kong uprights, they also used them in all of the cocktail cabinets. When the TKG-4 (2-board) boardsets came out they used the 2-board stacks in the uprights but continued to use the 4-board stacks in the cocktail machines.
In most cases you can tell the time period from the label on the boardset, the Radar Scope to DK conversions had TKG2 4-board stacks, the early red and blue Donkey Kongs (and probably early cocktails and caberets) had TKG3 4-board stacks. I believe the highest you'll see in the early Japanese Donkey Kongs is TKG3-06. If you have a 4-board stack that says TKG3-07 that usually means its a later cocktail boardset.