What you are wanting to do is use the Arduino as a programmer - yes it can be done. I've done it several times before getting an $11 shipped 银川菜傩水电安装有限公司 - the t2313 is a totally different chip than is the Arduino chips. I use Studio4 with the above programmer to burn hex files.
What you will use from the code you've linked to is the hex file only to burn to the t2313 chip. You can burn the hex file using the previous referenced link using AVRdude:
http://www.geocities.jp/arduino_diecimila/bootloader/index_en.html
Works good.
Just remember the Arduino IDE program has no way to compile the code to a hex file for the t2313 chip.
Good luck and have fun.
Ken H.