Sounds a lot like mine, although it's always tricky to tell with sound recordings like this. I'd say mine probably sounded worse when it was brand new. I might be able to detect a slight tick in that recording, but probably not.
I’ve come to accept it’s a ‘feature’ rather than a fault, due to a load of factors such as thinwall cylinder blocks, lean burn combustion, not much soundproofing under the bonnet, loads of thin plastic and metal parts on the engine and exhaust. At the MOT last December (1st one at my friendly local place) the tester thought it was a diesel at first.....
From inside the car, windows up of course, it just sounds a bit ‘gruff’ when you do hear it.
The first time I heard mine run was when I collected it from the dealer. You can just imagine how bad it sounded as it started up inside the glass palace.....
I think it was quieter after I took it back and they apparently applied an update to the ECU, but never totally convinced it wasn't just some BS from the dealer to shut me up and get rid of me.
Ultimately, it sounds pretty rubbish IMO. I have a 1996 or so vintage Ford Zetec engine in our Westfield which is almost silent, mechanically, even in a plastic car with zero soundproofing. I have a 2001 vintage Alfa V6 in the other car I built recently and that sounds awesome compared to the MB. Even at idle the V6 sounds better than the MB.
No denying the MB engine is clever, but I don’t think they put much effort into what it sounds like.