The salient points are:
* Very small N.
* Behavioral studies of mice can be very subjective in their own right, so you can definitely get bias, particularly with small N.
* There's no generally accepted model of autism in mice. In other words, mice might not even be capable of getting autism in the first place, so saying that "these behaviors in mice correlate with autism in humans" is a bit of a limb.
* No measurement of the microbiome in the descendants-of-the-implanted-microbiome (the ones that were actually tested) was demonstrated.
So you can come away from the paper with the feeling that they set out to test a hypothesis, interpreted subjective results in the way that best matches the hypothesis, and failed to (or perhaps even purposefully excluded) test for alternate hypotheses that might explain the evidence better.