EU laws mean that UK and for that matter German or Italian or any other member states companies may tender for ANY Government contract in ANY member state.
If Eastern/Loganair or OLT want to tender for Irish domestic PSO grant supported air traffic routes they can do so.
Now if they need to be short listed and there is a pre-tender process (usually is) -This process can weed out weaknesses in their suitabilty to meet the tender specification.
If the specification is well worded (within a legal framework) then the actually choice of tenderers can be made very narrow indeed effectively excluding the likes of Eastern/Loganair and others and THIS IS QUITE LEGAL.