You haven't yet proven that it's a working circuit as just reading the voltages without load current being drawn is a very incomplete 'test'. I would suspect you might find problems when there are unequal load currents being drawn from the two different voltage outputs. So be sure to test by measuring the two voltage output value with one voltage rail supplying say 200ma and the other 100ma and see if the voltages change or not.
I have seen many DC voltage 'rail splitter' designs in the past, some very cleaver, but most with some limitation or other. So perhaps you have indeed come across the simplest voltage rail splitter design to date, but I would suspect you would need to show more evidence to convince some of us. The lack of a true balanced ground connection is very suspicious to me.
In you schematic you have a 24vdc voltage source driving a negative and positive voltage regulators. Now do you mean to tell us that if you hook your volt meter to the +15 and -15 terminals that you will get a 30vdc reading? ( a true dual polarity DC power supply will read 30vdc directly across the two output terminals) How is that possible with using a 24vdc source? Remember that any circuit connect must use just the single ground terminal output pin and one or the other or both output voltage terminals.
Good luck and keep us posted on your results.
Lefty