Do I need to leave the Terminal 3 for a boarding pass at Beijing Capital Airport?

You have no need to leave the terminal and you can check-in in T3. You could do as the following:
Arrive at the International Arrival Level at 3F of T3-E → accept Health & Quarantine → Inspection → go through the Entry Frontier Inspection → take APM at 2F of T3-E to reach 2F of T3-C → go to the International Baggage Claim Hall → go through the Animal & Plant Quarantine (sample check) → accept the Customs Inspection located north of the International Baggage Claim Hall → enter into the I-D Transfer Hall → finish domestic flights transfer procedures & deliver baggage → take the special elevator upstairs to 3F of T3-C → pass the Domestic Security Inspection →Waiting & boarding