Songwriters mostly get paid for "mechanicals" these days - royalties on recorded performances. Some also get paid for specific public performances but to get this implies that you actually sold them decent notation with which to produce said performance along with a license to perform it.
Probably 90% of the tabs on these sites are for songs not published in sheet music form. Most of the stuff is there for instructional use. The only way to learn how to play well is to play a lot of different stuff. If you have to license all this stuff to learn to play an instrument, one day there will be no musicians (heck, we're nearly there now). This law will destroy the final remnants of culture if fully enforced (impossible I know).
In fact, since the beginning, pro musicians have circumvented this kind of nonsense with underground traded "fake books" (a large book of popular songs with lyrics and general cord structures - enough for any reasonably accomplished musician to "fake" his way through the song and get that $20 tip in the lounge for playing some yahoo's request). Fake books were for sold with a nudge and a wink under the counter of most sheet music establishments.
Given that this was the model before, I see no reason why it will change with a bunch of laywers running around threatening skilled people trying to help the younger talent come up.
The whole thing is anti-american.