Larry has given you the best advice for native MS Project functionality. Task Path provides a very welcome graphical addition, but you can’t group or sort based on it.
Sorting by logical path is a natural output of recursive logic tracing routines. If you are comfortable with vba (macro language), here’s a link to a set of macros on my blog that automatically filter and sort for task path. I grabbed your pen example (with completely imaginary durations) to illustrate the concept. Here it is sorted by ID, sorted by Start, and filtered/sorted by the QTraceP (i.e. quick trace predecessors) macro.
If you’d rather not mess with vba, I use an add-in called BPC Logic Filter that can generate nearly identical output.