In addition to making runners look kind of goofy and making viewers think athletes are injured and wearing kinesio tape, Nike's AeroSwift tape makes a competitive difference. Just not much of one.
To start, we take the claimed advantage given in the Competitor article - "a 2-3 percent drop in wind resistance." This seems sort of small, but at the professional level every little bit does count. For the calculation I assume a 2.65% reduction in drag because it gives nice round numbers.
We then find from Pugh (in the conclusion if you're interested) that while running at 6 m/s, wind resistance accounts for 7.5% of the total energy expenditure over the course of a race. It just so happens that this is almost PERFECTLY in line with the pace that won Galen the 10,000m at the trials, his speed was 10,000m/1,675s = 5.97 m/s. In addition we can draw similar conclusions about the 5,000m and marathon since Lagat won the 5,000m with an average speed of 6.13 m/s and Galen won the marathon with an average speed of 5.36 m/s. Although the marathon pace is a little farther away from the 6 m/s number quoted by Pugh than I would like, I still believe it is comparable enough for these purposes.
Having the percent effect on overall work by drag and the percent reduction in drag caused by the tape, we can now calculate how quickly someone would run at the same effort level with and without tape.
With a 2.65% reduction in drag, the total reduction in work for a runner wearing tape relative to a runner not wearing tape is 1-0.075*0.0265 = 0.998. So over the same distance, a runner with tape will only exert 99.8% the work as a runner without tape. Assuming the same amount of work done by both runners, the taped runner will reach the finish in 99.8% the time it takes the non-taped runner to complete the course.
Let's see what difference 0.2% in finish time would make at the trials:
5,000m: Lagat goes from 13:35.5 to 13:33.9
10,000m: Rupp goes from 27:55.0 to 27.58.4*
Marathon: Rupp goes from 2:11:12 to 2:10:56
So... not much. That's less than 1 s/mile pace difference. So, the tape saves a little less than 1 s/mile in distance races which is nowhere even remotely close to the savings you can make by drafting. According to Pugh, there is a 20% decrease in drag when drafting a similarly sized runner. 20% is obviously much larger than 2-3%.
So, the real effects of wearing Nike's AeroSwift tape on pace at the top tier of the sport are less than 1 s/mile when running in the open, and approximately no effect when drafting. If we really "want" to see a difference then the tape is most effective in the open so it is possible that athletes wearing the tape may feel more confident trying to break the field open and worrying less about drafting. I doubt this will be reality however. The largest difference we are likely to see is an ever so slightly more relaxed Rupp at the end of the marathon where everyone has 25 miles at 4:55 in their legs and Rupp only has 10 4:55 miles in him, the other 15 being at a mere 4:56 jog.
It should be noted that I am not knocking the tape, just putting it in perspective. I love the fact that Nike continually tries to innovate, looking for every possible advantage, I think that's a good thing for the sport. But the reality of this specific improvement is that the effects will only be psychological.
*Rupp's 10,000m time increased since he wore the tape in this race, so I "took the tape off him" in this calculation.