"Intelligible" is far from binary-- there's a huge middle ground between being able to figure out some words, and having it sound basically normal to you. If you heard someone speaking Chaucer's English you would probably be able to get the general gist, but it would sound weird and you would miss a lot of words. That's middle English, from about 1400.

Shakespeare is about 200 years later, and you've probably heard some Shakespeare aloud. For most contemporary English speakers, Shakespeare is hard and weird, but especially in dialogue when it is less formal, they understand almost all of it.

And by another hundred years or so after that, grammar and syntax and vocabulary were all very similar to ours, so you probably would have thought that the person talks a little funny, but had no real problems communicating.