Lower bound on independence number in terms of clique number and order of graph
Where it says

then any maximal independent set has size at least $n^{1/k}$,


it should say

then any maximal independent set has size at least the floor of $n^{1/k}$,


(Then this sentence is true for the complete graph $K_k$.)

They are being a bit sloppy, but I imagine that they just need the result for "large enough $n$".