The "-2" in -2dr/r is the -2 in the tidal tensor and represents the stretching effect along the axis of attraction, as represented by the first order term of the power series expansion.
The displacement is considered "slight" in the sense that the first order term is much larger than higher order terms.
Also, whether one uses higher order terms or not, the whole treatment is of a differential force.
The speculation in this article -- while wildly wrong -- does not involve tidal forces.
It says, " This rare alignment will mean that the combined gravitational force of the two planets would exert a stronger tidal pull, ..." Sheesh!
There are no tidal forces involved in the phenomenon described.
The article clearly says if you jump you will take longer to come down; that isn't a tidal effect. A tidal effect would be that the wrinkles on your face form more slowly than the wrinkles on your toes, or that water splashed into the air will form slightly more elongated bubbles during this alignment. [AND ... Neither of these things happens because even with planetary sized bodies tidal effects are, within experimental error, entirely first order effects.]
The -2 in the -2dr/r is not a tensor. The expression is just the differential: d(2Gm1m2/r2) Unless you're claiming that scalars are tensors. OK, they are. But no actual physicist calls a scalar a tensor. As a matter of fact the first order term in the expansion is a vector, and it points radially, and again, nobody but the prissiest mathematician on the planet actually calls a vector a first order tensor.
In any event, you are simply wrong. This article talks about a "tidal" effect to give it an air of authority, but the effect described is not the least bit tidal. It's simply a gravitational effect, and about 15 orders of magnitude smaller than claimed.