The relatively cheap UPS models meant for routers/networking hardware work brilliantly for the Pi. Something like this can typically run the Pi for several hours or more (depending on capacity) without AC before giving up. It's also largely the same cost as the Anker you are looking at.

I have a Pi, router and modem on something like this and can get 3-4 hours during power cuts.

I have two UPS in the house. One large APC for my main workstation (PC, Monitors, secondary access point, SmartThings, MyQ, Printer, HTPC).

What I was more surprised to find was this UPS when I converted my phone jacks around the house (wired with cat5e) to ethernet. This one is wall mounted (awesome!) in my garage along with a router, switch, modem, and patch panel for the house wiring. It's a nice and cheap option for battery backup on simple devices. NOTE: Grounded devices cannot be plugged into this UPS.

You can get a real UPS for not much more than the cost of a power bank (and less than many), and it'll actually work like a UPS is supposed to, switching you from mains to battery and back. A power bank will always run off of the battery, and then charge itself separately. Even if your power bank can discharge while charging (most don't), you're wasting power 100% of the time because the conversion from mains to battery is not 100% efficient.

APC makes a UPS just for this purpose. You can buy it here on Amazon. I bought one of these just to run my modem and it lasted me through the entire time my power was out (which was over 3.5 hours) with battery left over. So I think it'll give you more run time than any other general purpose UPS out there. Mind you, it does not support anything with grounding prongs and it has a max capacity of somewhere around 70W, so don't put anything extra on it besides the modem and the RT-AC68U. The reason why it can achieve so much runtime for its size is because it was specifically designed for such low loads and has a very efficient dc to ac inverter. Another thing to note is that this thing can only output a square wave, so don't put any sensitive equipment behind it (the modem and router are most likely fine). They also have a cheaper version [here] (https://www.amazon.com/APC-BGE70-Back-UPS-3-outlet-Uninterruptible/dp/B00KH07WRC/ref=sr_1_1?ie=UTF8&qid=1479869782&sr=8-1&keywords=APC+bge70) that has a little less runtime and is probably cheaper than any normal UPS, I think this would be the best option as you're looking for just 10 mins of runtime anyway (it advertises to do 3 hours).

EMCXRKBE2

for easy copypasta
Today only (2017-09-14, ends 11:59:59 PDT or before). Email says this is targeted, so YMMV. I was able to use my shoprunner for free 2 day shipping, though shipping should be free regardless--just slower without SR, probably.

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Per the Amazon page (which actually has reviews) this will do a decent job of powering your modem & router through a brief power outage, as well as providing brown-out protection. Useful if you have a laptop or tablet to use during a power outage, and/or your main PC with UPS isn't located in the same place as your networking.

For reference, here's the Amazon price history: https://camelcamelcamel.com/APC-Back-UPS-Connect-Battery-BGE70/product/B00KH07WRC

So this?

https://www.amazon.com/gp/aw/d/B00KH07WRC/ref=mp_s_a_1_2?ie=UTF8&qid=1498345538&sr=1-2&pi=AC_SX236_SY340_FMwebp_QL65&keywords=small+ups&dpPl=1&dpID=41Di53n5qML&ref=plSrch

??

edit: oh yeah i just realized the APC Back-UPS Connect UPS doesn't have a ground prong

I'd say you're better off with one of these that keeps the internet on even during an outage http://www.amazon.com/APC-BGE70-Back-UPS-3-outlet-Uninterruptible/dp/B00KH07WRC?ie=UTF8&psc=1&redirect=true&ref_=oh_aui_detailpage_o04_s00

I bought mine for $19.99 a couple weeks ago but now they're $37 apparently but still a nice thing to have.