"Gripping" means "exciting" "breathtaking" (a "gripping" plot or movie, for example). "Grip" literally means to hold or grab, so if something is "gripping" it is holding your interest. Here, though, it is probably meant sarcastically and thus implies that whoever the person is whose life is being described as "gripping" actually has a very boring life (irony!).

I haven't read the book or diary, but I would think it means: "What an exciting life you lead".