I really can't think of how they would stop this.

Like genuinely.

The sites that manage these gambling rings aren't owned by Valve, and reporting the sites doesn't get them taken down by the domain providers.

In Steam the trades look the same as any regular trades between players, so if they wanted to stop the gambling trades it would require turning off all trades.

Do you know if anyone has come up with some way they could track and stop the gambling sites?