The curse of the ground loop
The first one uses a star grounding scheme, which works well in some circumstances: low frequencies, absence of incoming EMI/RFI... which means it is an increasingly less useful scheme in today's world...

However, before talking about the loop, I'd like to point out that your design is single-supply, thus chips draw supply current and dumps it into the ground. Using long traces for GND in this case means this current will create a voltage against the GND impedance. Since GND is used as a voltage reference, your chips will have different reference potentials.

If these are single-supply opamps, they will process this as signal. If they are logic chips, ground bounce can corrupt logic levels.

In both cases a low ground impedance is beneficial, ie. ground plane. Without a ground plane you can route horizontally on toplayer, vertically on bottom layer, and create a grid of supply/ground, which was popular back in the days of huge boards packed full of TTL chips.

Note that if your chips are +/-15V opamps, then current flows into the supplies, but they are not connected to ground (except via decoupling caps) so in this case the varying supply current will only introduce extra noise on GND if the decoupling caps are badly placed/routed.

Now, back to your question:

There is no proper solution to this. Back in the day of single-sided analog boards (think a VCR or a tape deck), they were usually placed inside a metallic enclosure which acted as a shield, and there were no cellphones. Today's hifi stuff (for example) will usually have some shielding, if the faceplate is plastic, then you can expect a bit of conductive spray paint to shield against incoming EMI.

Also, these huge TTL logic boards were designed before modern electromagnetic compatibility directives, and frequencies were low.

Anyway. If the signals are fast, then they need to be routed close to the ground return current path, or else a loop antenna is formed, which will both transmit and receive, also the extra inductance will corrupt the signal itself.

Thus, if these are logic chips, the last layout in your post would be preferable. In fact, the "ground loop" would be one cell in an oldskool "grid ground/supply" board.

Note that the ground loop is a shorted turn, so incoming RF would have to be pretty strong to induce a high enough voltage into it to corrupt logic levels. The main problem would be that it would have a resonant frequency somewhere in the spectrum...

Now, specifically about audio grounding, I can only recommend this article from Bruno "The Man" Putzeys. Also valid for other analog applications. It is also a fun read.