Those lights are 18 Watts per meter. 18 watts on 12 volts is 1.5 amps. Those strips are 1 meter each. 10 strips is 10 meters. 10 of those strips would consume 15 amps. That power supply probably can power those strips but it is right at the limit of the power supply so you may have problems. I'd recommend a 20 amp power supply instead so you have 5 amps headroom.
It’s weird, I googled but still absolutely no review yet.
I intend to connect one terminal to the PSU output then run a cable all the way (10 metres) to the other end to connect to the other terminal. The point is to eliminate voltage drop at the end of the strip. Since it is 15 amps plus, what kind of wire gauge should I use?
I don't know how much power those bars consume; the listing doesn't say anything about it, but I assume they're 1.5 amps. If all those bars in total draws 15 amps then that power supply should be fine.
You should connect each individual strip directly to the power supply, not connect them end to end, because the strips wouldn't handle high currents like 15 amps through them.
20 or 22 gauge wire should be good if you connect each strip directly to the PSU.
You could also line two wires alongside the strips, like a power tap or whatever it's called, and connect each end of each strips to the wires. Then you don't need a lot of small wires all over the place. If you do this, you need 12 gauge wire (20 amps max). 14 gauge (15 amps max) wouldn't be good because the wires would be at their limits and to be safe you should use 12 gauge. And the power supply is 20 amps too.
I think the second idea is better. String two 12-gauge wires alongside the strip, and connect each end of each strip to them.