Without thinking ahead I bought this TBS8922 DVB card:
After that I found that my motherboard has PCI 1x slots like below. Also, their end is opened.
Can above card plug into this socket?
You have a PCIe x1 slot. PCIe is a modern standard
The card is a PCI card. This is a very old standard, and not physically compatible with PCIe. Some modern motherboards still come with PCI slots, but that's not what's in your photo.
It is possible to get adapters, but that tends to be a bit messy and rather expensive. If the card isn't particularly expensive, you're probably better off buying a PCIe version of it.
No, one is PCI the other looks like a pcie x1 slot.
https://www.startech.com/Cards-Adapters/Slot-Extension/PCI-Express-to-PCI-Adapter-Card~PEX1PCI1
These adapters exist, but a new tuner might be a similar in cost.