I've checked and it works fine in both WMS and WMTS. Attached is a zipped .map with the WMTS version.
As the Comments in that project discuss, this is very cool data and a very generous effort that is marred by an unfortunate misuse of EPSG.
The layers from the Eox WMTS server (same in the WMS service) are available in two forms: one which uses the EPSG:4326, Latitude / Longitude coordinate system, and a "3857" version that claims to use Pseudo-Mercator like Google. Besides the main "cloudless" work product there are many very cool and useful accessory layers.
However, only those two "3857" layers that are found in GoogleMapsCompatible subfolders:
...are actually in the EPSG:3857 coordinate system used by Google, etc. Lucky for those seeking a good "cloudless" data set, the main work product correctly uses EPSG:3857.
All of the other "3857" layers use a fake "EPSG" code of 900913. There is no such EPSG code in the EPSG database and never has been. 900913 is "google" spelled as numbers (the "9" looks like a "g") and was used by some people as a name for what they thought was Google's coordinate system before EPSG:3857 became the universal standard for Google-style Pseudo-Mercator. But "900913" is not the same coordinate system as EPSG:3857.
Therefore, except for the two "3857" layers which correctly use EPSG:3857 you should always use the non-3857 layer versions. Those are in Latitude / Longitude but Future will re-project those on the fly so you can use them together with genuine EPSG:3857 layers like Google with no problem.
Hopefully, Eox will fix the problem so their "3857" layers use EPSG:3857 and not a fake 900913 code. This project will not need to change when they do that since the project gets all coordinate system information from the Eox servers on the fly.
It will be easy to check if Eox has fixed the fake-code problem:
Open the "3857" layer of interest and see what the Contents pane reports for the coordinate system. If it reports Pseudo Mercator (EPSG:90913) in red letters you know they haven't corrected the data set. If it reports WGS 84 / Pseudo-Mercator (EPSG:3857) in black letters you know they have corrected the problem.
Until the "3857" layers get corrected, just use the Lat / Lon versions of those layers (most of them) which do not correctly use 3857.
Anyway, this is a very generous service from Eox for which they should be commended. Yeah, some of the layers don't use 3857 correctly but that's no big deal given they thoughtfully provided lat/lon versions as well. I'm confident they'll get it fixed quickly.
s2 EOX server.zip