You have a Mini-PCIe card (for a laptop).
You're trying to put it in a full size PCIe slot (which looks like a desktop motherboard).
Laptops have mini-PCI slots. Desktops have the full size PCIe slot.
That said, you can still do it, you just need one of these. Search for "Mini-PCIE to PCIE adapter". As you can see they make kinds that have wiring for external antennas.
I've noticed some desktop motherboards have one actual Mini-PCI slots for Bluetooth/wireless cards - but yours may not. So you would need one these adapters.

PCIe has a concept called "lanes" - x1, x4, x8, x16 refer to the number of "lanes" the connector has. More lanes = faster.
Graphics cards typically are x16 (the full length) and the longest slot is intended for those types of cards. Less bandwidth-intensive cards like RAID or Wi-Fi require less PCIe bandwidth and so can use the smaller slots.
The CPU has a limited number of lanes it can support (32, 48) so all slots usually aren't x16 (unless you don't want other peripherals than graphics cards).
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If I follow your link I see a full size PCIe x16 slot, a full sized PCI-e x1 slot, a full sized PCI-e x1 slot, and no ** mini PCI-e slots. While the card is not PCI-e but MINI PCI-e. the manual confirms this.
– Hennes – 2017-12-23T19:22:49.223