How to achieve short journal names in this bibliography style using Biblatex package?

You can transfer data from one field to another using the Biber source map feature:

\DeclareSourcemap{
  \maps[datatype=bibtex]{
    \map[overwrite]{ % Notice the overwrite: replace one field with another
      \step[fieldsource=shortjournal,fieldtarget=journaltitle]
    }
  }  
}

See for example \DeclareSourcemap in biblatex for more on this feature. Mappings only apply if the source is available, so this is 'safe' for cases where there is no short title.