Is it because of the tuning of the strings, what the strings are made of, or the shape of it? Or something completely else? Would it be possible to replicate the sound with a regular guitar?
That's a very broad question with no single answer. There are dozens of instruments unique to the Far East, and some may sound more "exotic" or "Eastern" than others do.
Three things occur to me:
1) Traditional Asian music uses different scales and tunings than Western music does. Indeed, traditional Chinese music has had various systems of 12-note scales, 13-note scales, and 5-note scales, and they can sound quite different than the chromatic 12-note scale that is familiar to the Western ear. You can read more about that here: https://en.wikipedia.org/wiki/Chinese_musicology
2) The materials and technology used for making traditional Asian instruments would vary greatly from instrument-making in Europe over the last several centuries. Types of wood and metal would vary greatly, as well as animal hides (I just read that shamisen traditionally uses cat or dog skin!) and materials for making strings and bows. An example of this would be bamboo, readily available in Asia, which naturally lends itself to making flutes and other wind instruments. The sonic characteristics of a bamboo flute would be quite different from a wooden flute made in Europe. And yes, what the strings are made out of can cause a huge difference in sound. For example, compare the coiled steel strings of an acoustic guitar to the nylon strings of a classical guitar.
3) Different styles of music dictate the types of instruments that get built. There is probably no better example of this than the Western classical symphony. Through the centuries, the European composer has pushed the boundaries of instrumentation. Families of related instruments, such as violins, violas, cello, and bass, were designed with similar tunings, so as to make life easier for both the composer and the conductor. These instruments were built to sound good together, and master craftsmen spent a great deal of energy making sure timbre and tonality were pleasing. Ultimately, these instruments have come to sound "Western."
In the case of the shamisen, the biggest difference between how it sounds from a guitar is that the shamisen is fretless. You could likely get a (somewhat) similar sound on a Western instrument that doesn't have frets, such as a viola or fretless electric bass. Or you could get one of these: