Can i remove this from my desktop to instal a Video card???

Yes you can remove that card to install a graphic card. Make sure you get a low profile card for that slimline PC.

This is from the manual

As a matter of fact it mentions the modem card so this is expected.

Removing and Replacing a PCI Card

You can also replace the modem card in the PCI card slot with another modem card or a new PCI card. The modem card is a telephone modem circuit board that fits into a PCI card slot.

Before You Begin

Observe the following requirements before removing and replacing the component:

IMPORTANT: Due to the small PC size, you can only install a small, low-profile PCI card of the same approximate size of the modem card. HP recommends that you install a card with power consumption of 5 watts or less.

Not all low-profile cards will fit into the PCI slot. Some external connectors, especially connectors located at the top of the card, may not fit properly into the back panel.

This procedure requires a Phillips screwdriver.

Removing a PCI Card

1 Prepare the PC and remove the PC cover. Complete the “Opening the PC” procedures on page 2.

2 Inside the PC, locate the PCI card slot on the motherboard.

3 Make a note of any internal cables attached to the card, and then disconnect them.

4 Remove the screw on the modem card bracket holder (A) on the outside of the frame. Remove the bracket holder.

5 Hold the card at the top and carefully pull the card straight out of the slot (B).

16 Upgrading and Servicing Guide

Replacing a PCI Card

You can replace the modem card with a new modem card or another PCI card in the PCI card slot:

1 Complete the procedures to remove the modem card. See “Removing a PCI Card” on page 16.

2 Align the edge of the add-in card with the slot on the PC and gently but firmly press the card straight down into the card slot (A). The whole connector should be seated properly in the card slot.

3 Attach the bracket holder with the screw to secure the card (B).

4 Connect any internal cables attached to the card.

5 Complete the procedures to close the PC. See “Closing the PC” on page 5.

6 Install any software drivers— supplied by the card manufacturer if you are installing another PCI card— or as required.

NOTE: If the new card or device isn’t working, read the card manufacturer’s installation instructions, and recheck all connections, including those to the card, power supply, keyboard, and monitor.

You can take the modem out if you do not need it but :

1. You may void your warranty

2. The video card needs to be small enough to fit in the case.

Yes you can.