ByteDance Ltd., the China-based owner of TikTok, is starting to snare market share in the virtual-reality headset space that Meta Platforms Inc. META -2.12%decrease; red down pointing triangle has identified as critical to its future. Two years ago, ByteDance bought Pico, a Chinese startup that makes VR headsets. That launched a new front in the Chinese company’s competition with Meta META -2.12%decrease; red down pointing triangle, whose Instagram and Facebook services have been battling for users and advertising dollars against TikTok as the short-video app soared in popularity.