[NTP] Reorder shortcuts on dragstart instead of mousedown

Start the reorder flow on dragstart instead of mousedown. This will
prevent the tile from showing its elevated state when the user clicks
it. As a side effect, the elevated state will not appear until the user
starts dragging the tile.

Screencast: https://drive.google.com/open?id=1Oy6dK-2r8TwdC1XW6ka0LRy676mpDXTG

Bug: 986741
Change-Id: Iada5fefcade302b815b9fbaf1582ae00cac57b24
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1717146
Auto-Submit: Kristi Park <kristipark@chromium.org>
Commit-Queue: Kyle Milka <kmilka@chromium.org>
Reviewed-by: Kyle Milka <kmilka@chromium.org>
Cr-Commit-Position: refs/heads/master@{#680593}

chrome/browser/resources/local_ntp/most_visited_single.js

@@ -1096,12 +1096,8 @@ function stopReorder(tile) {
  */
 function setupReorder(tile) {
   // Starts the reorder flow.
-  tile.addEventListener('mousedown', (event) => {
-    // Do not reorder if the edit menu was clicked or if ctrl/shift/alt/meta is
-    // also held down.
-    if (event.button == 0 /* LEFT CLICK */ && !event.ctrlKey &&
-        !event.shiftKey && !event.altKey && !event.metaKey &&
-        !event.target.classList.contains(CLASSES.MD_MENU) && !reordering) {
+  tile.addEventListener('dragstart', (event) => {
+    if (!reordering) {
       startReorder(tile);
     }
   });