The setup can be quite tricky. Keep in mind that the dependency logic is essentially embedded in the javascript.  It's crucial to follow the instructions EXACTLY.

• the dropdowns must be set to "autocomplete" edit type
• The 3rd parameter of set_col_edittype() must contain an ENTIRE string of all the "key:value" pair of that column

Let's dig deeper.

In the demo, $countryStateData is an array (array() replaced with shorthand [ ] for brevity) that contains two countries, 'usa' and 'canada' where each contains its states in sub-array respectively. This is the data to populate the first dropdown.

The second array $stateCityData contains the state details which are going to be displayed in the second dropdown, which is the nested dropdown.

$countryStateData =
    [
        'usa' => [
            ['id'=>'', 'text'=>''],
            ['id'=>'ca', 'text'=>'CA'],
            ['id'=>'al', 'text'=>'AL'],
            ['id'=>'nj', 'text'=>'NJ']
        ],
        'canada' => [
            ['id'=>'', 'text'=>''],
            ['id'=>'ab', 'text'=>'AB'],
            ['id'=>'qc', 'text'=>'QC'],
            ['id'=>'bc', 'text'=>'BC']
        ]
    ];

$stateCityData =
    [
        'ca' => [
            ['id'=>'', 'text'=>''],
            ['id'=>'ca', 'text'=>'San Francisco'],
            ['id'=>'al', 'text'=>'Los Angeles'],
            ['id'=>'nj', 'text'=>'San Diego']
        ],
        'al' => [
            ['id'=>'', 'text'=>''],
            ['id'=>'ab', 'text'=>'test'],
            ['id'=>'qc', 'text'=>'test2'],
            ['id'=>'bc', 'text'=>'city2']
        ],
        'bc' => [
            ['id'=>'', 'text'=>''],
            ['id'=>'ab', 'text'=>'2342344'],
            ['id'=>'qc', 'text'=>'bc city2'],
            ['id'=>'bc', 'text'=>'bc city333']
        ]
    ];

Call set_col_edittype() on both dropdown and set them to autocomplete as shown below. The 3rd parameter must contain the ENTIRE "key:value" pair of that column. In other words, not only Country dropdown must contain the key pair value of all the countries, the States dropdown must contain "key:value" pair for all the states including both USA and Canada, merged all in one "key:value" pair string.

$dg->set_col_edittype('state', 'autocomplete', ':;bc:BC;ab:AB;qc:QC;al:AL;nj:NJ;ca:CA;Co. Cork:Co. Cork;CT:CT;Isle of Wight:Isle of Wight;MA:MA;NH:NH;NSW:NSW;NV:NV;NY:NY;Osaka:Osaka;PA:PA;Pretoria:Pretoria;Québec:Québec;Queensland:Queensland;Tokyo:Tokyo;Victoria:Victoria');