Please include any time when they stated a falsifiable claim.
They claim that global warming is man-made. This is a falsifiable claim: with enough understanding of the climate you can either find an alternative mechanism which is the cause of the heating or you can understand the man-made mechanism in enough detail that there is no room for doubt. This is not at all easy but there is no requirement that things be easily falsifiable.
So, if it gets hotter, it's global warming, if it gets colder, it's global warming. In the end, there's no way to prove it wrong. By your own definition, that's not science.
The climate is a complex beast and disturbing it can easily cause local cooling even if the overall global trend is to warm up. For example if the melting Greenland ice cap dumps enough fresh water into the Atlantic to disrupt the Gulf Stream then northern Europe will get a LOT colder. If there are reasonable, verifiable mechanisms for local then it is not unreasonable to have local cooling caused by global heating.
If you want to attack this survey then there are far better way to do it: which journals did they use and are they reputable? were the search criteria biased in any way and were control samples using a random selection of articles without the initial selection bias checked for a consistent result? Even if the survey was completely unbiased in every way can you really draw any sensible conclusions from numbers of papers?
As a scientist what I truly find really objectionable though is that this is science! You should make up your mind based on evidence not on what other people's opinions are: this is not some popularity contest! Personally I think the evidence for global warming is overwhelming and it is highly likely that humans are some or all of the reason behind it but don't believe me: I could easily be wrong! Listen to what the evidence is and make up your own mind.