First of all, the link you've provided is not the official Nanoblock website, it is a fansite. Nanoblock is owned by the Japanese toy company Kawada, and the official website can be found here.
That means that this is not an official claim from Nanoblock. However, it is true that Nanoblock bricks do not infringe on any copyright, and not only because Nanoblock bricks are smaller than Lego.
The relevant patent for interlinking blocks that we all think of as Lego expired back in 1978. Since then, Lego has repeatedly taken companies to court for trademark violations, but in recent years this has largely failed. Judges have repeatedly ruled that the interlinking studs are a functional design, and not eligible for trademark protections.
The same is not true for Minifigures, which are still protected by an active trademark, as well as product lines like Ninjago.
Lego was successful in shutting down some copycat companies like the Lepin in China after years of legal battles, but that was for blatantly copying Lego IP, from builds to box art.
Nowadays there are plenty of reputable alternative brick brands creating original sets that do not infringe on any copyright or trademark protections, even if they are the same size as Lego bricks.