They've done a few things.
They became a sponsor at EVO and gave Melee their blessing, which was a nice gesture after last year's fiasco. The entire Smash scene is a grass roots endeavor, and they always felt Nintendo didn't care. Seeing them sponsor a tournament shows they do.
They hosted an official tournament to showcase Smash 4 and invited several competitive Smash players. Many people were surprised that an "official Smash tournament" could even exist.
There isn't an online mode that matches tournament rules, but there's something close with "For Glory", which allows you to match random people 1 on 1 with no items on Final Destination. Since competitive Smash uses more stages than Final Destination (Which gives a major advantage to certain characters), you'll really only get that experience playing with friends where you can set the rules. Still, it's a really good gesture and it will introduce more people into the competitive scene if they like For Glory.
No idea about the online lag, but it's almost certainly going to be better than Brawl's shit online.
In general, the game seems to have more of a competitive focus than Brawl. Randomization is reduced in characters, random tripping is gone, speed is increased in most areas, ledge camping is gone, the game has more balancers, etc. It's unknown how well this will work, but it's clear they care.
Overall, Nintendo has done a good job of roping back in the competitive scene after Brawl alienated so many.