Two spacing originally came to be because of typewriters, which had to give the same amount of space to every letter. Modern word processing isn't under such an impediment, and so the space between letters is set to equal in most modern fonts (so the letter 'M' gets more space than the letter 'I'). In this arrangement, the second space after a period isn't as important, because your can more easily differentiate the end of words and sentences.
This study seems hardly definitive to me, with two big issues. The first is that the group that saw improvement were people who had been taught double spacing. So they have a pre-disposition to it. Ideally, the study would include both groups of people.
Secondly, the study used a monospaced font, the same as a typewriter. That is effectively imposing the weaknesses of a typewriter on modern typography. If you impose the weaknesses of the past on the present, you will generally find the solutions of the past to be effective.