That's an apples-to-oranges comparison, though. The 10^-70 number is a relative error while the planck length is just a length. The numerical computations in the paper were likely done in a system of "simulation units" where the actual lengths, velocities, forces, etc. are normalized to values of order unity. This has advantages for the numerical aspect, in terms of preserving floating point accuracy. But it also means that to translate it to a physical system (e.g., a triple system of stars), the simulation needs to be scaled to physical units. The 10^-70 that's quoted just means that the values should be numerically accurate to 1 part in 10^70.

If you wanted to compare the (floating point) accuracy of the simulation with the Planck length, you would need to scale the simulation to a physical size and see what the 10^-70 fractional error would translate to in physical units.