Deservedly, imho
Pinter's been a vital figure in theater--especially British theater, of course--for decades, but his influence goes far beyond his wonderful plays. I think it'd be difficult to overstate his importance to the worldwide creative community.
Years ago, a noted actor once referred to realistic drama (which is what we North Americans typically see on TV or at the movies) as "a small room with a low ceiling." Pinter helped show us there are much larger rooms to explore.