They are both under the jurisdiction of the US federal court system. Something applying to the white house means it applies to individual states as well.
If the case was decided on 1st amendment grounds, it's absolutely true.
Edit: not necessarily saying they should, I’m just wondering if they can.
Edit 2: Looks like the most they could do is make it harder for social media companies in general to do business. If they were perceived as targeting Twitter then they could have grounds to sue.
Based on 20 minutes of reading so grain of salt applies.