The PC has a free PCIe x16 slot, but it is not specified whether it has a PCIe x1 slot. The Hauppauge WinTV QuadHD card requires a PCIe x1 slot, and the maximum length of the cards at the rear is 7 cm. The case is compact (29.5 cm x 10 cm x 33 cm), which limits the space available for expansion cards.

It is therefore likely that the Hauppauge WinTV QuadHD PCIe x1 card can be installed if the PC has an accessible PCIe x1 slot and if the card is no longer than 7 cm. However, this precise information on the presence and location of a PCIe x1 slot is not confirmed in the available data.

I advise you to check directly in the case or the detailed technical documentation of the PC for the presence of a PCIe x1 slot and the space available for the expansion card before purchasing.