If you can schedule a PEK-HKG flight on CZ with departure about 2-3 hours after the KLM arrival at good price, do that. It will keep everything in T2 and likely you could interline luggage on Skyteam partners KLM->CZ and avoid the baggage pickup/recheck step. But even if you must pick up, not a big issue. Immigration as described above and on the FAQ under TWOV (transit without visa).

If price/availability has you purchasing a ticket on Air China, Cathay Pacific or Dragonair to HKG, you'll be leaving from T3 and will need to shuttle between the 2 terminals on the free shuttle bus. With this sort of transfer on non-partners, you might not be able to interline (though try it anyway) and will need to pick up luggage at T2 and take on shuttle bus to T3. Buy a ticket that allows you at least 3 scheduled hours to do this. It's not that the actual process takes that long...but sometimes PEK has air traffic delays into (and out of) so I put a little flex time into my estimates to accommodate that.

If you happen to schedule a longer layover in PEK--say 6-7+ hours that are during the day/early evening, you can also check-in or put luggage in Left Luggage and go into the city to sightsee. No visa required as long as your arrival->departure is less than 24 hours.