Anyone can give some info, why the ground ring is required for the RTC around its crystal pins?

As Erik already stated, it has to do with EMI:
A typical RTC chip is designed to work needing ultra low power supply current. This can only be accomplished, if internal CMOS circuitry is very high impedant, means, if outputs of logical gates are high impedant. Compared to 74HCMOS gates, which show an output impedance of about 50Ohms, logic gates of an RTC presents dozens of kiloohms or more.
Unfortunately, with this increase of output impedance a powerful weapon against injection of digital switching noise loses its strength: While with 74HCMOS noise would be shunted via output impedance of 50Ohm to ground (or Vcc, which also means ground because of decoupling capacitor), with high impedant output impedance such a noise shunting doesn't work. And finally all the noise would be coupled into the crystal circuitry.

At least two things can happen if digital noise with high voltage change rate is coupled into RTC via crystal circuitry:

1. Stored information can be corrupted, if the noise even penetrates the memory.
2. More or less drastical shift of oscillation frequency, means a loss of precisison of RTC.

With a ground ring arround crystal pins, a guard is introduced. Means, the digital circuitry in the neighbourhood can no longer inject noise into the RTC. Instead, the awful noise is injected directly into the ground ring.

This guarding technique is very effective and should never be omitted! But don't forget also to provide real good power supply decoupling measures for this RTC chip.

Kai