The 7 round limit is likely a very clever and underhanded ploy. If passed it would be another example why pro-gun rights people are so wary of claims of "common sense" and compromise.
There was never any real logic behind the 10 round magazine limit. Some people feel the number came from a gun maker, Bill Ruger. The story is Ruger's Mini-14 sales were suffering due to imports of semi-automatic rifles of similar size and weight. Ruger's rifle used a 10 round magazine. The imports used more than 10 rounds. Ruger suggested a 10 round limit because it would allow him to keep selling his rifle while stifling the competition. Many gun people still curse his name for it. I have no idea if this story is actually true or if, like the Nova not selling in Mexico because of its name, it has become a legend that won't die.
Regardless, if you ask someone who is in favor of these laws how many rounds would they want if they had just a gun to protect themselves you will find they are more likely than not going to ask for all they can practically have. Even on this forum you will find such an answer.
So back to why 7. That's easy. It's rare for any modern semi-automatic gun to have just 7 rounds. Most will have at least 8 and often more than 10. The 1994 magazine limit meant that manufactures had to produce 10 round mags so they did. That equipment is still in use for states like CA that have 10 round limits. NY is a relatively small gun market. A 7 round magazine is yet another thing for a gun maker to deal with. Most will simply say, forget it, it's not worth the trouble and won't sell in NY. Hence the state has created an economic disincentive for the gun makers.
It's not clear what will be a legal retrofit for a 10 round magazine. Can the owner just add a block or is it something more complex.
Overall this seems like a VERY stupid law. For example, why raise the penalties for carrying a gun onto school property? The previous penalties would keep any honest gun owner at bay. The person looking to commit a crime won't worry about the stricter new penalties. Basically this whole law won't do the things it claims to do but will further erode the rights of legal gun owners.