Burnley were arguing last year - but it didn't get to court - that Everton's FFP issues were not adequately dealt with, so are joining with this season's relegated threatened clubs to sue PL who are now in the cross fire.
Burnley's case is that relegation triggered the immediate repayment of a loan in turn causing losses elsewhere as assets needed to be sild to repay the loan (ie consequential losses etc. Plus of course Everton got 'their' share of PL revenues versus a parachute payment to Burnley) with Burnley also losing gate and sponsor revenues by being a Championship club versus a PL club.
The clubs threatened with relegation will not, as you say, all be relegated but they are all joining the action so as to maximise pressure on PL as even though a couple might escape they all want rules tightened up so Everton (and others) cannot dance round FFP whilst other clubs get relegated.
The court case is about PL enforcing the rules or not - so judgement will be received by all the clubs. In terms of compensation the main beneficiaries if they win will be Burnley and the relegated clubs - but others might be able to argue that being so close to relegation they lose sponsors, chances of signing players etc and be able to persuade court they have had losses which need compensation.
I think PL will try to avoid a court case (especially as Man City FFP case re-opened) so we might only hear the headlines of any settlement outside court