Gleb Bahmutov's tutorial demonstrates how to verify the sorting functionality of an Ag-Grid table using Cypress for testing. The example involves an HTML file that creates a "smart" table widget with sortable columns for car make and price, utilizing vanilla JavaScript. The test begins by loading the table and ensuring the presence of three rows, then verifies sorting by price. Despite visual confirmation of sorting through the UI, the initial test fails due to Ag-Grid's use of the translateY property to reposition rows without altering the DOM order. The test is refined by attaching a row index attribute from the parent element and converting price text to numbers for accurate verification of sorted order, ultimately passing when the list of prices aligns with the expected sorted order. This exercise highlights the importance of understanding DOM manipulation in testing dynamic table functionalities.