ALERT: READ the bottom part - I may have to revise all this, depending on what OP can report.
Some confusion and misinformation among these. I do see what has been raised as a small issue - there appears to be NO Ground wire in the box, even though the outlet fixture does have a Ground terminal. That may be because the cables in the wall from the breaker panel do not have any bare Ground wire, OR it may be because that Ground wire is there and is only connected to the BOX itself and not continued on to the screw terminal of the fixture. In the latter case it will still function, because the construction of the outlet fixture itself means the metal mounting frame of it is also part of the Ground screw and Ground (round) hole in the outlet.
Even if there is NO Ground connection to this box and outlet fixture, that is NOT a problem here. A GFCI device does NOT need a true Ground to operate. The safety protection it provides depends on measuring the currents flowing in the Hot and Neutral lines and verifying that they match very closely. Unbalance is taken as evidence of improper current leakage out of the circuit, casing the device to trip. That is why one use of GFCI devices in older homes with NO Ground wires in the cables is simply to replace the old (often 2-prong) outlet. The result of that "upgrade" does provide protection against improper current flow in a manner that is different from what a Grounded outlet can do, even though such a circuit does not provide a true Ground at the outlet.
OP, as others have said, this appears to be an "end of line" switch installation. That is, power to this lighting circuit is fed from your breaker panel to the ceiling light fixture box, and then a second cable comes from that box down to this switch box. In the ceiling box, the Hot feed line bypasses the light fixture and is just fed on to your switch box on the Black wire; the White Neutral line in the ceiling box is fed to BOTH the light fixture and the White wire coming down to this switch box. The old device you are trying to replace has three wires to it: Black (to the screw labelled "Common Feed") is Hot from the breaker panel via the ceiling box, White is Neutral from that ceiling box, and Red is the Switched Hot - the output from the switch portion to take power back up to the light fixture elsewhere. Looking now at the diagram for the new GFCI Switch / outlet combo device, it uses the labels LINE for the oncoming source of power (Black Hot and White Neutral) and LOAD for the output of power going back to the ceiling box. So, connections are:
BLACK to the LINE Hot Terminal (Brass) screw
WHITE to the LINE White Terminal (Silver) screw
RED to the LOAD Hot Terminal (Brass) screw
You do NOT need to make any connection to the LOAD White Terminal (Silver) screw that is covered with a Yellow sticker. And since you do not appear to have any bare copper Ground wire on the box, you make no connection to the device's Green Ground screw.
Internally in that device, the LINE Hot and Neutral wires are connected to the outlet portion permanently so they are always on. The Hot line is connected also through the switch portion to the Load output terminal (Red wire) so the switch can control power sent back to the ceiling light fixture.
WAIT!!
I may have misunderstood the labels and connections on the diagram for the new replacement GFCI device!
OP, the diagram also includes two black lines at top right labelled "Switch Leads" that I do not understand. So, some questions for you to answer.
1. Are there really two wires leading out from that area? If so, what colours are they?
2. Are there any other instructions for this device beyond that diagram you showed? Does it tell you what to connect where?
3. Look closely at the side with the two BRASS screws. Are those two completely separate, OR is there a metal "bridge" connecting them together?
Depending on what you can tell us, my advice above may be wrong regarding the connection details, and require revision. So please post further info. The wiring diagram that ch33zw1z posted above for a Leviton device looks VERY like your diagram, and has better instructions.