Mobile data plans are cheap enough and good enough that most people, even travellers use them now. Enforcing this law could simply get free anonymous wifi turned off so all traffic goes over the mobile networks.
Edit: found it. https://www.theguardian.com/world/2016/aug/10/thai-regulator...
Edit: to clarify I don’t think the two are linked specifically - most services/purchases like this in Thailand require some form of Government ID. For locals that’s usually an ID card, some places will accept my Thai drivers licence others want passport.