In an interview with CVG, Sony Computer Entertainment America's marketing VP John Koller explained that, apart from the PlayStation 4 and perhaps the PlayStation Vita, a Dualshock 3 controller will be necessary to stream titles via PlayStation Now.
When asked about controller input for PS3 games on a tablet and the DualShock 3 controllers being used at the Bravia TV demo stations at Sony's booth at CEX 2014, he responds:
It needs to go through the DualShock. The DualShock remains the key ingredient. So that controller experience needs to go perfectly. We didn't want to utilise touch screen or anything like that because the games are best played with a DualShock...
The DualShock 3 specifically. To enable tablet and smartphone play, you've got to have the DualShock 3.
This is a relief, at least for me since I own five (count 'em, five!) Dualshock 3 controllers. The wireless nature and easily recharged battery should complement PS Now on tablets and smartphones nicely.
The DualShock 4 controller will be all that's necessary for PS Now on PS4 and the Vita controller inputs seem to be fine on their own as well, though without the L2/R2 trigger buttons, some titles may not work so well.