我认为这个问题与HERE API无关，而是与Javascript本身有关。
我在https://www.w3schools.com/howto/howto_js_fullscreen.asp和Failed to execute 'requestFullScreen' on 'Element': API can only be initiated by a user gesture上找到了解决方案
测试的简单代码：

function openFullscreen(elem) {
    if (elem.requestFullscreen) {
      elem.requestFullscreen();
    } else if (elem.webkitRequestFullscreen) { /* Safari */
      elem.webkitRequestFullscreen();
    } else if (elem.msRequestFullscreen) { /* IE11 */
      elem.msRequestFullscreen();
    }
  }

 //when you tap on screen then is opened in fullscreen mode
 map.addEventListener('tap', () => {
      openFullscreen(document.documentElement); //open in fullscreen mode whole HTML document
      //or
      //openFullscreen(document.getElementById('mapContainer')); //open in fullscreen mode only map
      
    });

以上示例在此处实现：https://jsfiddle.net/ybj57ovc/1/