This is a pretty bad analysis.
First, there's no control, so we have no idea if the level of "dog anxiety" is actually higher among hugged dogs than non-hugged dogs--imagine that non-hugged dogs are always anxious, but hugging them lowers their anxiety level so that some are not. Imagine alternatively that the anxiety is real, but that the thing making them anxious is having their photo taken and we have no control in terms of dogs not having their photo taken. No treatment effect can be identified.
Second, there appears to be significant measurement error. "Dog anxiety" is operationalized as a three point scale: no anxiety, neutral anxiety, or some anxiety -- and we don't know the coding rubric the coder used to decide which category to put it in. It's not even clear if there is a standard, academically accepted dog anxiety rubric. I do not believe it is the case that dogs closing their eyes indicates anxiety. Normally in studies of this type that rely on coder discretion for a noisy response parameter, we have two coders and rely on inter-coder reliability scores to debias estimates. But even if we assumed the measurement was good and there was a control group, the study would have very little power because the score only takes three values so it's unlikely even doing it properly and then trying to grab a difference of means between treatment and control would get you any results.
Third, there's no reason to believe the photos were selected randomly because it's entirely possible that the same characteristics that make the coder see anxiety are also characteristics that search results select on on the basis of image quality (for example, "half moon eyes" might be anxiety to the coder but an easy to identify feature for Google's Image search.
Finally, this is a blog post, not a journal, so it's arguable whether or not this is even research versus just "something to do on your lunch break". It's not peer reviewed, it's probably not edited, no one else is cited, it's not building off any research, it's just a "hmmm... some dogs in photos look anxious..." observation.