You should come here and do a simple “(external) ATF cooler” search here instead of Google the entire Internet for the questions you have on possibility of installing an external ATF cooler to Mazda’s SkyActiv-Drive 6-speed automatic transmission.
For SkyActiv-Drive transmission an ATF cooler is piggybacked to the transmission.
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The difference comparing to other automatic transmissions, such as the YouTube video you posted for a Mazda5, is SkyActiv-Drive pulls engine coolant into the ATF cooler to cool down the ATF which is also circulating into the ATF cooler "internally". Two lines attached to ATF cooler outside are engine coolant instead of ATF lines circulating out into the radiator or an external ATF cooler found on most other vehicles. The traditional aftermarket external ATF cooler relies on those external ATF lines to circulate the fluid into external air-cooled heat exchanger cooling down the ATF. . Since SkyActiv-Drive transmission doesn't have that, an aftermarket external ATF cooler can’t be installed unless you get a special ATF cooler adapter which comes with external ATF cooler kit.
There're modified transmission coolers adding two ATF ports commercially available for other vehicles with similar design mainly on CVT's. With this ATF cooler adapter, we can hook up an aftermarket external ATF cooler easily:
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And here’s an ATF cooler adapter for Mazda’s SkyActiv-Drive transmission only for ATF flushing purpose:
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What have you done to your CX-5 today?
2016.5 CX-5 Transmission fluid change questions
ATF flush adapter