Why is Ni[(PPh₃)₂Cl₂] tetrahedral?
We sometimes call this type of complex 'pseudotetrahedral' since there is an isomerism from a tetrahedral to a square planar complex possible. I was unable to find the original work here but this link gives some information. As you already mentioned there are two strong and two weak ligands so it's hard to tell how strong the ligand field splitting will be. For your particular complex it seems to be right on the spot where it would change from one to the other so depending on what you do you can influence the equilibrium. From what I read this may depend on the ability of the solvent to coordinate to the complex as well, the temperature, etc. 

This is also mentioned in Earnshaw's Chemistry of the elements


  
  Planar-tetrahedral equilibria. Compounds
  such as $\ce{[NiBr2(PEtPh2)2]}$ mentioned above as
  well as a number of sec-alkylsalicylaldiminato
  derivatives (i.e. Me in Fig. 27.6b replaced by
  a sec-alkyl group) dissolve in non-coordinating
  solvents such as chloroform or toluene to give
  solutions whose spectra and magnetic properties
  are temperature-dependent and indicate the presence
  of an equilibrium mixture of diamagnetic
  planar and paramagnetic tetrahedral molecules.