One thing about their cord construction is it is using two wires only.
More than half of all the radios that chirp supports use two-wire communication (all Icoms, Alincos, most Yaesus).
Is there no error correction for the data
What does error correction have to do with how many wires are being used? No radio (or serial device) I've ever seen uses actual error *correction* over the line. However, several do employ error *detection* through the use of checksums. All Icom radios provide this, but only a sprinkling of the other radios do.
or is it being written in half duplex or just how exactly does serial data flow over two wires. ?
The TX and RX lines are tied together, which means that when either side transmits, they see their own data reflected back. It is indeed half duplex, and requires either end to "chew up" these echoes in order to read a subsequent response from the other side. It's a fairly common thing for simple serial devices. All the CAT bus radios do it this way, for example. If you have a big HF rig that communicates with an amp or an antenna tuner, it's doing the same thing.
It's kinda funny to spend $60 for an OEM programming cable that only has two wires inside, huh? :)