To download all objects using wget:

wget -r -H -N --cut-dirs=4 --include-directories="/v1/" "https://swiftbrowser.dkrz.de/public/dkrz_1e33ba3a-9ecb-452f-93b9-583cf4a66e57/ICON-HDCP2-DE/20160526-default-cont_month?show_all"

Name
20160526-default-cont_month
_overview_rain_clouds_winds_perturbations_20160526-20150530.mp4