The Hamlet Project

This is very odd. Very odd.
What IS Claudius responding to here? And which Claudius is this?
I mean – I’d expect Claudius to say something like, “Come on, Hamlet, stop messing around.”
But he doesn’t. He says, “Alas, alas!”
Which is really more like something Gertrude would say.
It feels like he might be putting on a show of grief. But who is the show for? Hamlet?
Rosencrantz and Guildenstern? He didn’t say, “Alas, alas!” to them.
It’s just such an oddly out of character thing to say.