Yes a survey was the method used to gather the data. Same as that used when doing polling data prior to an election or post-voting exit polls to determine which candidate is winning an election.
This was a scientific survey. Not sure where you are getting that it wasn't. Pew Research Center is one of if not the leading think tank regarding looking at the public's attitudes and trends that take place in the country. This wasn't done as some 6th grade project.
Read their methodology and tell me their method isn't scientific:
http://www.people-press.org/methodology/
In addition, as I said before they can't survey every adult. 1) Legally you can't force every adult to participate and answer your questions 2) Financially it would be prohibitive to ask +300 million people questions 3) It would be time consuming and data intense to deal with all the data.
That is why you do data sampling and surveys. If it was done correctly (I trust Pew), then their sample should be well representative of the population as a whole. So you make sure you have a broad representation of different education level groups, incomes, regions, ages, genders...etc. From that (if the sampling was done correctly), you can infer what the rest of the population is like.
This survey had over 9,500 adults in it. You know those presidential polls you read about, they typically have around 1,000 adults.
You can definitely take a survey and if done correctly, draw inference to what the rest of the population is like. i.e. the rest of the population is the market.
So this is definitely a valid representation of the marketshare of tablets.