I like that it solves the problem of getting the mass up over the bulk of the atmosphere before you have to give up giving it any more energy. If you could mechanically build the thing (it looks to be on par with a space elevator in terms of material requirements) I don't see any obvious violations of the laws of physics.
Space elevators would be preferable from a footprint perspective caveat the seemingly infinite tensile strength cables.
I think that the Lofstrom loop is way more realistic than an orbital elevator, mainly because the cables "only" need to span ~100km, rather than the ~36,000km required for a geostationary elevator.
Also, I see that there are improvements in that part of the design: the cables could be replaced with counterweights, and those counterweights could be accelerated upwards and dropped, in order to dampen the waves generated by the release of vehicles.
I don't see why this has a flattened middle segment at all - wouldn't it work better if it was a continuous parabolic arc, like an elliptical orbit that intersects the Earth at the locations of the base stations? That way, the working mass wouldn't have to make sharp turns wherever support cables are pulling on the loop.
For a relatively near-term non-rocket launch system I like Hans Moravec's rotating skyhooks. Similar to a space elevator but less of a leap. If you can get one going around each of the earth and the moon then you could power operations from then on by dropping moon rocks down to earth.
Space elevators would be preferable from a footprint perspective caveat the seemingly infinite tensile strength cables.