I recently looked up whether there are Epcots at other disneylands/worlds and nothing came up on the internet, but I am curious as to whether there are other facilities similar to Epcot where there are some countries on showcase. Particularly, I am curious about Japan, since I'm going there soon, but I would love to know about ones in other countries.
Not in Disney Complexes.
The Tokyo Disney Complex (Land, Sea, Hotels, Resort) does not have an Epcot Centre. The Epcot Centre in Orlando was actually built concurrently with Tokyo Disneyland. Further, the Epcot Centre idea was originally abandoned on Walt Disney's death having actually been a plan for a self sufficient city. When Disney revisited the idea, they scaled it back to merely a theme-park-sized rather than a city-sized project.
Specifically in Japan (Tokyo), you may look for something like the Miraikan in Odaiba run by the National Museum of Emerging Science and Innovation, which showcases new and emerging technologies from Japanese companies and universities.
If you wish to experience foreign culture in a Theme Park format then Shima Spain Mura is where you get to experience Spanish Culture. It is between Kyoto and Nagoya (about 2hrs train ride from either) and has mascots and characters reminiscent of Disney characters.