Your pictures do not show where the connectors from the displays are attached. Those will BOTH be plugged into the graphics card, which is plugged into the PCI card slots. If you look on the back panel again, you will see where your displays are plugged in the back. Trace the cables from your displays. You will see where they are connected...
The first set of pictures (which you said you downloaded from the web) - the 2nd picture shows where you would plug in displays. YOUR video card is slightly different, and would have two connectors that are the white rectangle with all the holes (there's about 28, with 4 of those around a plus (+) )
Your picture shows a newer version of that card with only one of those multi-hole connectors, and two more that are much smaller. You don't have THAT card, your's has two of those 28-pin (DVI) connectors, and that's it.
And, There's no HDMI ports to see (you didn't miss any, because your Mac Pro doesn't have any HDMI ports.)
To connect your TV (with HDMI as the only choice) you will need an adapter cable, such as
this one - which has a DVI connector for the MacPro, and an HDMI connector for the TV.
(This cable is for video ONLY, no audio, so you would need to connect an audio cable from the MacPro to the TV audio input. Your MacPro has digital audio out, and TV has digital audio input. I would suggest that you use that connection for sound from the MacPro to the TV. )
Finally, I am sure that graphics card will support two displays. If you want to have the TV connected, then you would need to decide which of the other two displays to disconnect.
The only way to have both displays, and the TV all connected and usable, is to add a second graphics card. Your 12-year-old Mac Pro is fairly limited to what it will support for graphics cards, so I suggest that if you want to do that, come back here to get some possible cards to add to your system.