Since the implementations in each language/framework are all available, you can look into the few that seem the most interesting base don your own criteria and get a quick idea of whether you think they would be a good fit for your criteria.
In that respect, I think the benchmarks can be taken seriously, as long as you don't their rankings to be an indicator of what's best. That is, don't consider it a benchmark, consider it a very thorough survey of available frameworks.
However, it's not that benchmarks are meaningless -- review their methods. If you can think of a way to test that they're not following, or find some flaw in their testing methodology, then tell them about it, and have them fix it (or post what's wrong somewhere), but they are pretty up front about HOW they test, so results should not surprise you, given enough knowledge of the frameworks involved (if they test something that flask is great at and tornado is not, that will be obvious given knowledge of how the test was conducted)
Why are you even using Python if you are worried about performance?
However I would have liked to take advantage of Tornado's asynchronous requests handling thus my disappointment with its performance in the said benchmarks. I wanted to avoid using "uwsgi" with Flask because of an already complex technology stack i.e: Nginx + uwsgi + Flask + zeromq + Go + sql/nosql database(s)