Because the hosts are part of the defendants.
A party in a lawsuit can demand documents to be turned over to them from the opposing party. That is called Discovery and participation is mandatory. Not turning over the documents requested and not providing a good reason why they should not be turned over is contempt of court.
Discovery under the Federal Rules is very broad. According to Rule 26(b)(1), "Parties may obtain discovery regarding any non-privileged matter that is relevant to any party's claim or defense." The federal rules also provide several tools that can be used to get information from other parties, including interrogatories, depositions, and requests for admission. A party may also compel other parties to give them access to documents, real property, or other things for review or testing. See Rules 26-37.
The Delaware rules of Civil Procedure mimic the Federal Rules of Civil Procedure very closely, and their Rule 26 is close to the Federal Rule 34. Especially interesting here is:
Del. R. Civ. P. Super. Ct. 26 (b) (1) In general. - Parties may obtain discovery regarding any non-privileged matter that is relevant to any party's claim or defense and proportional to the needs of the case, including the existence, description, nature, custody, condition and location of any documents, electronically stored information (EST), or tangible things and the identity and location of persons having knowledge of any discoverable matter. It is not ground for objection that the information sought will be inadmissible at the trial. [...]
The hosts are employees of the defendant, the phones contain EST that is regarding the matter and relevant to Dominion's claim, and disclosure is proportional to the needs of the case. As such, The employer has to make them comply with discovery requests by the opposing party and hand over the text messages.