Vlookup - create new list from existing list based on partial match

If you can use helper columns, populate column G, for example with this formula in G3 and copy down:

=IF(COUNTIF(A3,"*"&$E$3&"*"),A3,"")

Then use this array formula (ctrl+shift+enter) in H3 and copy down:
=IFERROR(INDEX($G$3:$G$14,MATCH(1,(COUNTIF(H$2:H2,$G$3:$G$14)=0)*($G$3:$G$14<>""),0)),"")

And finally this lookup formula in I3 and down:
=IFERROR(INDEX($B$3:$B$14,MATCH(H3,$A$3:$A$14,0)),"")