Is the Choice operator implementable on $\pi$-calculus?
The issue is that you are manipulating $\oplus$ but you don't have any rules (besides its definition) telling you what reductions you can do. The whole point of the paragraph that presents this definition is that there are multiple notions of choice and some but not all are encodable.


  Many process calculi have explicit choice or summation operators for
  nondeterminism, allowing for example $P+Q$ which can behave either as
  $P$ or as $Q$ (this is imprecise – in fact several different operators
  are possible).  [...] In some cases a form of choice is encodable
  in a choice-free calculus – for example a purely internal choice can
  be encoded in the π-calculus given in Section 1.1 above by [expression from question] but 
  in  other  cases  non-encodability  results  can  be  proved [...].