Based on this question, it seems that delta-shaped wings do not perform well at low airspeeds. But why do paper airplanes, particularly the most well known one, fly well even though the airspeed they fly in is at most 15 knots on average?
Your interpretation of the answer to that question is a bit wrong.
It would be an error to claim that delta wings don't perform well at low speed. Delta wings perform exceptionally well at low speeds.
The correct interpretation is delta wings are not fuel efficient. And this is true at low and high speeds.
There are advantages to delta wings at both high and low speeds. The following list are some of the known advantages:
Improved handling at high Mach numbers due to swept leading edge (note: this is the same advantage as swept wings but with the down side of being draggy when performing manoeuvres - swept wing planes retain much more kinetic energy after a turn).
Intrinsically strong structurally (it's a triangle!) thus can be built much lighter.
Retains quite a lot of rudder effectiveness at low speeds and high angles of attack (this is unintuitive because you'd think the wing would block airflow to the rudder but the strong vortex shedding on the leading edge maintains flow around the rudder).
Have very wide CG range compared to conventional aircraft. This is especially useful in bombers.
Have very benign and gentle stall behaviour. This is especially useful for paper airplanes since it can prolong flight at low speeds (paper airplanes simply dip their noses and regain speed instead of simply diving and crashing).
The major disadvantage is that it is draggy. Thus not fuel efficient. Thus in a business world where profit and cost matters delta wings are not attractive.
For supersonic flights the drag is apparently roughly on par with swept wings. Except, as mentioned above, due to the geometry of the wing it can be built lighter thus save fuel - so it sort of cancels out.
For toy planes, where efficiency is not of great concern (fun and "cool" is more important) delta wings are OK.
Still, if you use the same sheet of paper and built a long, narrow, cambered wing like this:
.. you'll find that the long narrow winged plane flies much further than the delta wing paper airplane given the same launch speed.
Delta wings don't perform well at low speeds compared to other low speed wings such as straight ones. The delta wings do have some disadvantages compared to the 'reguar' wings at low speeds. I'm assuming that you're talking about paper aircraft like this:
Image from secretprojects.co.uk
Delta wings have more friction drag, have difficulty in integrating high lift devices and have low AR etc. (as already noted in that question); however, most of these disadvantages are marginal when it comes to the paper aircraft. On the other hand, this kind of design offers some good advantages when you want it to just fly when thrown:
The delta wings still produce lift using a vortex, which means that they stall at much higher angles of attack. At low Reynolds numbers, the max. lift coeffecient is obtained at slightly higher AoA. This helps in their flight.
The centerfold, in addition to helping in holding and throwing, also helps in lateral stability. Also, the flow through that helps in reducing the pressure over the top surface of the paper craft, helping in increasing lift.
They don't perform well on paper airplanes as compared with custom engineered airplane's made from single or ply sheets of paper.
It's just that it's much easier to fold a sheet of paper into a delta wing shaped airplane; hence the reasons most paper airplane shoes have delta wings on them.