Why does one combine PCR and cloning as ways for amplification of sequences?
There are several reasons to clone a PCR product but the main reasons include expressing the product and maintaining the library inexpensively. 

In the study you mentioned, the cloning and transformation is apparently done for obtaining single clones (from single colonies). 


  Clones were picked randomly and colony PCR was then performed using
  vector primers T7 and SP6 to amplify the cloned inserts. Cycle
  sequencing was performed using BigDye version 1.1 (Applied Biosystems)
  and an automated capillary DNA sequencer Genetic Analyzer 3100
  (Applied Biosystems).


Since the original PCR would have a mix of different sequences, cloning is done to separate them out for the ease of studying them by sequencing. If they don't separate the sequences, they would have to use NGS (or more expensive methods like PacBio for longer reads). They have used Sanger sequencing. This article was published in 2007. At that time NGS was not as cheap as it is today and was hence not used by everyone. Also, the NGS machines of that time had even smaller read lengths (~40 for Solexa/Illumina GA and ~75 for GA-II). Considering these, Sanger sequencing may have been preferable to the authors of this paper. However, as I mentioned before, Sanger's method cannot be used for sequencing pooled samples; you need pure templates or else there will be mixed signals and base calling would be inaccurate. 

(See the example chromatogram below: look at the position with the Y which has mixed T and C signals. It is not from a pooled sample, though).


Therefore cloning, transformation and colony picking was necessary.

Moreover, in many cases picking individual clones would be necessary for performing functional assays to associate phenotype with genotype.