"Why is Alola Exeggutor Grass/Dragon type?" Power Swap. Back in 4th gen, I had a Sunny Day Doubles team with Exeggutor: It would use Leaf Storm, then Power Swap to simultaneously give its lowered SpAtk to an opponent and restore its own SpAtk. Sometimes it would also be passing off Intimidate debuffs or stealing Swords Dances or whatever. Good times. Anyway, Alola Exeggutor can most likely have both Leaf Storm and Draco Meteor, making this little gimmick far more versatile. That's likely the idea here.
"Why is Alola Sandslash Ice/Steel type?" Ice Ball + Gyro Ball. This is less certain, since Alola Sandshrew's description says it can't roll itself into a ball, but I wouldn't be surprised if it could still learn Defense Curl, Ice Ball, and Gyro Ball anyway, since it can curl itself into that spinning curling stone as seen in the trailer. And if the description's correct about its Speed being lower than Sandslash's, that's another boost for Gyro Ball on top of STAB.
I'm not saying that these gimmicks will necessarily be competitively viable, but I'm pretty sure this is GameFreak's line of thinking. It's similar to how lots of the 6th-gen mega-evolutions tried to push a specific gimmick, like Volt Switch Mega Manectric, Me First Mega Absol, and Bullet Seed/Rock Blast/Pin Missile Mega Heracross.
I have no idea if Mega Ninetales has such a gimmick. Any ideas?