As you point out, rainbow tables are fundamentally about chains of hashes, and about saving only the entry points into those chains. One would never save every entry, and if one did it would not be a rainbow table. It's an arbitrary time-storage tradeoff, and faster GPU's simply change the "sweet spot". The limit is not the storage space, but remains the amount of time you are willing to spend pre-computing, and GPU's give you much greater leverage here.
I tried to look through the article and find some positive pieces to point out, but I couldn't do it. He the conflates floating point performance with hash speed, asserts that one needs to scan the full rainbow table from disk to use it, and concludes that rainbow tables are limited to 4 character passwords. The general conclusion is correct (worry about brute force attacks) but there are so many other large errors that I cringe in fear.
Author (should you read this): I don't mean be impolite, and I don't understand these issues well enough myself to try to teach them, but I truly am scared by your apparent fluency with these concepts combined with the level of inaccuracy. Please do what you can to keep educating yourself about these concepts before applying them professionally.