In Japanese, chesuto would be written チェスト, che-su-to. This is the only way the Japanese phonetic alphabet, katakana, can approximate the sound of the English word. So, the Japanese pronunciation of "chest" is heavily accented to follow the way it's written in Japanese.
If you're typing in a Roman alphabet, duplicating a bad Japanese accent on purpose has always struck me as kind of silly. The word is supposed to be "chest" so just write "chest" since this alphabet lets you write it correctly. People will know what you're talking about.
Yelling "chest" when you attack somebody is specific to the Japanese sport of kendo. Part of the rules of kendo state that you must call out which part of your opponent's body you're targeting. The Japanese use the English loan-word "chest!" to indicate an attack to the upper torso.
This isn't part of the Western sword-sport of fencing or, really, actual Japanese swordfighting (kenjutsu). Most modern Japanese know a lot more about kendo than they do kenjutsu, though, so swordsman characters like Sanger are often depicted as following the rules of kendo in their fights.