The extortion is this:
1. They were responsible, in part, for suing Company 1, presumably in the high-profile Monsanto lawsuits.
2. They offered Company 1 a deal: if Company 1 bribed them for $200M, they would deliberately throw the case.
3. Company 1 reported that misconduct to the DoJ.
4. Assuming Company 1 is Monsanto, the original lawsuits were successful; one case in particular awarded two plaintiffs $1B each.
The extortion here is that the lawyers were offering to throw the case and cost Company 1 only $200M instead of (presumably) $2B+, plus legal fees.
Bribery, on the other hand, under federal law requires that the person being bribed is a public official, outside of special provisions relating to sporting contests and port security (separate provisions, not common to those two circumstances.) Well, and one other inverted scenario involving Members of Congress, etc., bribing private entities by using official acts to sway hiring decisions on partisan political grounds. But nothing that seems applicable to the kind of thing going on here.