I suspect that the vast majority of websites won't do anything. Most websites are run by small and medium businesses, very small web design companies, private individuals, amateur bloggers, book groups, sewing circles, amateur dramatic societies, and the like. Only a tiny percentage of them will have heard this announcement. The vast majority wouldn't have a clue what it means, or how to go about implementing it. Most probably don't even understand what encryption is for - let alone what the difference is between HTTP and HTTPS.
What's more, for most users most of the time, encryption is irelevant. If you are looking for a carrot cake recipe, you want a recipe with easy-to-follow instructions, that uses common ingredients, that doesn't involve hours of work, and has a reasonable chance of producing an edible cake. The last thing you care about is whether the recipe was encrypted between the server and your computer. Someone is eavesdropping on the recipe? Who cares?
My bet is that, in six months time, this announcement will be completely forgotten. It won't change anything, either in Google's search results or the security measures that most website operators take.