There are without any doubt still tickets. Airline revenue accounts would fail without them.
When electronic tickets were first mooted several airlines saw it as a way of moving away from the constraint of 4 coupon tickets (a limitation imposed by biros and carbon paper). They proposed 99 coupon tickets. Revenue accountants then pointed out the cost of modifying their systems and the idea died rather quickly.
So, instead of printing the tickets everything that used to appear on a paper ticket is now stored in a separate database, away from the reservation.
If you look at the documentation that Swiss have sent you you'll find a 13 digit number beginning (if memory serves) 085. If all you are doing is travelling MAN/ZRH/HKG/ZRH/Man each passenger will have their own 13 digit number. Because one ticket still can't contain more than 4 flights if you were going on beyond HKG on the same ticket you'd each have two sequential ticket numbers (or 3 or 4).
If you are holding one ticket MAN/ZRH/MAN/ZRH/MAN and a separate ticket MAN/ZRH be ultra cautious when checking in at Manchester. If you don't check in for the MAN/ZRH flight that is on the MAN/ZRH/HKG ticket and check in instead for the MAN/ZRH separate ticket Swiss *WILL* cancel all your flights to HKG and back to MAN.
If your comment about having separate tickets means you have one ticket MAN/ZRH/MAN and another ZRH/HKG/MAN that is not a connection even though it may all be in one reservation. Swiss would be within the terms of their contract to refuse to through check you and insist you enter Switzerland, collect your bags and check in again and then go through security etc and if you miss the onward they would have no liability.