On this I can offer some generalities but understand IANAL.
There's a couple things to keep in mind... the rule system itself, Copyrights/trade dress, and the rule books. Game system mechanics themselves are not protected under current IP law... see the Hasbro/Kenzer Co. case for an example of that (Kenzer used mechanics from 2nd Edition D&D, got sued by Hasbro, and end up owning the rights to 2nd Edition D&D). This is also why you see collectible card games so very similar to MtG, board games that are copies of Monopoly, and so on. But Monopoly brings up the second part... Copyrights and trade dress. You can copy the mechanics, but the trade dress is what will bite you. If you use logos, copyrighted terminology, or anything else that defines the overall look or flavor... that's infringement. So while you can make a board game very similar to Monopoly, if the board too closely resembles the Monopoly board then you're infringing on their IP. And lastly there's the rule books... while you can quote from any book under fair use, extensive quoting/copying will get you in trouble.
How does that apply to Chummer and other character generators? Well, you'll note that Chummer hasn't and doesn't copy exact text from Shadowrun. The only current exception is for Mentor Spirit advantages & disadvantages and that will likely change to limit that text. Chummer also gives users the option to include and exclude content based on the book the material is from with the intention that users only use material from books they own. All of these measures are with the intention that users buy and own copies of the source books that provide the material and that without that material, Chummer itself doesn't provide enough information to use the rules from those books. As an example, Chummer now has the listings for the spells from Street Grimoire... listing information like its name, tags, and drain. But deliberately missing are the actual rules of what the spells do. So you can't really use them without the book.
I haven't looked in depth at Hero Lab or other generators but I'd imagine they're using the same system of limiting exact quotes from the books and not using trade dress unless they have a contract with Catalyst that permits it.