Do you mean you're interested in programming the ATtiny13A (so that it can talk to a target device, which happens to be a MCP23017 but that's not an important detail)?
Just guessing, HI2COUT might be the name of a memory-mapped register to output data to the I2C peripheral of a microprocessor. However, looking at the ATtiny13A data sheet and the MCP23017 data sheet, I can't see such a register named. Perhaps that is the name of a register for an I2C peripheral of a different type of microprocessor?
The MCP23017 has I2C hardware built-in--see section 1.3.2 "I2C Interface" starting on page 5 of the MCP23017 data sheet. It will tell you how to do I2C on that device. But assuming it's the ATtiny13A you want to program, it looks as though it has no I2C hardware, so as you say, bit-banging is needed.
I suggest doing an Internet search for "ATtiny13A i2c" and you should be able to find several examples.