This eliminates roughly 250 Pokemon from the tournament (including favorites like Blaziken, Excadrill, Breloom, Jellicent, and the Kami Trio), plus bans any Gen-V-or-earlier Move Tutor or TM move that can't be passed through breeding.
So. What does this do for the metagame? Protean Greninja with Mat Block will be everywhere, with the only Pokemon in this metagame that learn Mach Punch are the useless Ledian and Conkeldurr IF Timburr still learns Mach Punch as an egg move. Stealth Rock will be nearly nonexistent since it's no longer available as a TM move, leaving most of its users Rock- and Ground-Types (which die quickly from STAB Greninja/Azumarill/Gyarados/Blastoise) or Ferrothorn which is risky to use due to its speed and 4x Fire weakness (Talonflame, Mega Charizard Y, Moltres, Chandelure, etc.)
Klefki and male Meowstic become the only Pranksters, with Klefki having the clear advantage in typing, stats, and movepool. Drizzle Politoed is legal, making Rain teams an option (even with nerfed weather only lasting 5 turns). In rain, Mega Ampharos becomes a nasty threat and, since Drizzle+Swift Swim isn't banned in VGC, we get to face the wrath of Choice Specs Golduck (170 base Speed, 142 base Sp.Atk), Choice Band Floatzel (a ridiculous 230 base Speed, 157 base Attack, Crunch, STAB Return and Waterfall, and Power-Up Punch), and Kingdra (170 base Speed and good all-around stats, plus Flash Cannon to deal with annoying Fairies). In lieu of Swift Swim, 135 BP Surf plus Poliwrath, Vaporeon, or Quagsire with Water Absorb hits both enemies for STAB damage while healing you. Storm Drain, sadly, isn't available.
Toxicroak with Dry Skin heals up in rain as well, and even outside of rain, Fighting/Poison is a really good typing for this metagame, super-effectiving both annoying Steel- and Fairy-types, plus the large plethora of Grass-types. Skuntank may see some use as well, with its middling bulk mitigated somewhat by the fact that its only weakness (Ground) is weak in this metagame, with the prevalence of Greninja and Grass-types, and the only reliable Ground-type move the ally-hitting Earthquake. Skuntank can partner with a Steel-type (like, say, Aegislash) and soak the field in Poison with STAB Sludge Wave, or just STAB Poison Jab and Crunch with its respectable Attack stat. It can also learn Flamethrower and Explosion, so there's those too.
Sand teams can be led by Sand Stream Mega Tyranitar, but without Excadrill to show up and kill everyone, the only available Sand Rusher is the too-slow-to-really-make-use-of-it Sandslash. Hail teams might see some use with Snow Warning Aurorus and Mega Abomasnow, but Talonflame and Mega Charizard will outspeed both and pick them apart.
Trick Room teams gain Super Gourgeist, plus Mr. Mime and its brand-new Fairy typing. A Soundproofed Mr. Mime on a Trick Room team gains a nice partner in Scrappy Exploud and its STAB Boomburst.
Mega Mawile and its horrifying 210 base Attack will be a staple on Trick Room teams, and with its decent defenses and very nice typing, might even see some use outside of Trick Room.
Personally, I really like Exploud, but from the amount I've used him so far, Boomburst, even with Choice Specs, doesn't do as much damage as I'd hoped it would, thanks to Exploud's fairly mediocre Sp. Attack stat.
