I will paste the content discussed in the private thread here so the information is publicly available as well.
We do not have a built-in way to show the tooltip for overflowing text only, but I have opened a feature request to add this feature in the Kendo UI Tooltip component. Feel free to follow the request and/or leave any additional comments in the request for our developers. Based on the customer demand, feasibility, etc, the feature will be considered and added to our roadmap.