No, it does not at all require ByteDance to suspend service.

It requires Apple and Google to stop distributing the app on their app stores, and it requires any US-based hosting providers that host TikTok services to stop providing those services.

ByteDance could shut down any US-hosted services and serve from outside the US, and be entirely compliant with the law. The TikTok mobile app might become out of date and stop working (for people who already had it installed on their phones), but www.tiktok.com would continue to work just fine.