I do agree the whole paper is bull. Equations (1) and (2) are strictly speaking wrong, but you'd see these kinds of expressions if you are talking informally about these things. (1) should be a Riemann tensor, so its mostly wrong. For (2) it is a bit more general than R=0, since you could have Einsteinian manifolds and can make that redefinition. But yeah, without explaining anything, it's just nonsense.