If this connects directly to a PC serial cable, and assuming I'm correct that opto isolators have low R when LED on, high R when LED off ...
For RX/Serial In - When the RX line is high, Pin 2 must also be high. RX high, LED lights, transistor becomes a low R, Pin 2 pulled high - Looks like that is okay. With +12V on the RX line you may want a larger than 200R current limiting resistor.
For TX - When Pin 7 is high, TX line must also be high. When Pin 7 is high, LED off, transistor becomes high R, TX floats - That's also okay but you'll probably need a pull up resistor to +5V/+12V for the PC to register a high.