The study described is an observational study.
In this case, the website developer is not manipulating or randomly assigning participants to receive one of the website designs. Instead, she is selecting a sample of people who have already interacted with each design (those who reviewed design A and those who reviewed design B) and then surveying them about their opinions. There is no randomization involved in assigning participants to groups, which is a key characteristic of a randomized experiment. Therefore, this study qualifies as an observational study.