feat(ui): implement responsive player browser experience

docs/GAME_CORE.md

@@ -36,8 +36,8 @@ maze cells, static objects, and both current player positions.
 The serialized view is split into bounded JSON records of at most 512 bytes,
 matching the WebSocket gateway's message bound.
 Every record uses the architecture's versioned envelope and carries the
-authoritative state sequence, role, match phase, meeting sequence, chunk index,
-and chunk count. Role status appears once in chunk zero instead of being
+authoritative state sequence, role, match phase, maze width and height,
+meeting sequence, chunk index, and chunk count. Role status appears once in chunk zero instead of being
 duplicated across the snapshot. Cell records contain only the cell index and
 current passage flags. Object records contain kind, owner, variant, and cell
 index. Player records omit the `opponent` member when that player is not