Hi,
Yes, In Touch UI , there is resourceType "granite/ui/components/foundation/include" which is equivalent of cqinclude of classic UI.
Same as classic UI , there is path property whose value is equal to the path which you want to reuse. For ex: you want to reuse the dialog part "/apps/myproject/components/component1/cq:dialog/content/items/tabs/items/advanced" then this is the value to be used for path property. Do make sure not to use ".infinity.json" as it is not required in Touch UI dialogs.
Hope this helps!
Thank you!
Nupur