I'll be buying one of these, I heard it's really great.
The one linked looks to be a wired Powerline adapter. You plug one in near your router and wire it. You plug another in somewhere in the house and get an extended and usually a slightly weaker router port to wire something else up. Essentially it allows your wiring to carry internet signal and makes all your wiring live with internet. I do believe they have one that plugs in and picks up the signal to extend it though, like this
However they typically aren't recommended by enthusiasts versus 5Ghz wifi or a regular wired connection due to them being hit or miss. If your wiring is old they may perform poorly, if you're crossing multiple breakers or hit any interference they may perform poorly. Very few people get the same speeds they advertise (up to 500 Mbps) however they can be used in a pinch. I used one for my PC once upon a time and it worked well but now that I have 5Ghz ac wifi I use it because the speeds are about 20-30 Mbps faster for my downloads.
In your situation it may be worth a shot. If you don't like the performance you can always return it to Amazon stating you weren't happy with its performance.
You didn't pick a WiFI extender nor did you pick a kit (which has 2 adapters). You need one adapter at the router end and 1 adapter with the Wireless extender at the other end.
Here's the kit I purchased last year to extend the network in my son's apartment: TP-LINK TL-WPA4220KIT ADVANCED 300Mbps Universal WiFi Range Extender, Repeater, AV500 Powerline Edition, WiFi Clone Button, 2 LAN Ports
It's a medium speed kit - you can spend more for the faster protocols (AV2) but this kit should provide fast enough network to give you maximum through put on your wireless connection. It has a handy WiFi clone button which when pressed automatically clones the SSID on your existing wireless network.