If the 1st-stage gain is (say) 100 and, the 2nd-stage input offset voltage is (say) 10 mV, that offset voltage (when "referred" to the 1st-stage input) is 10 mV/100 = 0.1 mV.

So, if the 1st-stage also has an offset of 1 mV, then the overall offset voltage (including the 2nd-stage referred offset) is 1.1 mV at the input terminals.

On the other hand, if the gain of the 1st-stage is 20, the 2nd-stage offset referred to the input is now 0.5 mV and, this much more significant than when the 1st-stage gain was 100.

You could also refer offsets to the output and you would see that with more gain after an offset, the more significant it becomes as an error term.

What I am not understanding that how the offset voltage is related to intrinsic gain?

For intrinsic gain I assume you mean this line from your quote:

the \$g_mr_o\$ product is usually between about 20 and 100

If, the 1st-stage gain is 100 and, the 2nd-stage input offset voltage is (say) 10 mV, that offset voltage (when "referred" to the 1st-stage input) is 10 mV/100 = 0.1 mV.

So, if the 1st-stage also has an offset of 1 mV, then the overall offset voltage (including the 2nd-stage referred offset) is 1.1 mV at the input terminals.

In other words the 2nd-stage input offset has only a small effect on the overall input offset of the op-amp when the 1st-stage gain is 100.

On the other hand, if the gain of the 1st-stage is 20, the 2nd-stage offset referred to the input is now 0.5 mV and, this much more significant than when the 1st-stage gain was 100.

You could also refer offsets to the output and you would see that with more gain after an offset, the more significant it becomes as an error term.

If the gain of the 1st-stage is (say) 100 and, the offset voltage of the 2nd-stage is (say) 10 mV, that offset voltage referred to the 1st-stage input is 10 mV/100 = 0.1 mV. So, if the 1st-stage has an inherent offset of 1 mV, it can be seen that the overall offset voltage (including the 2nd-stage referred offset) is 1.1 mV.

On the other hand, if the gain of the 1st-stage is 20, the 2nd-stage offset referred to the input is now 0.5 mV and, this much more significant than when the 1st-stage gain was 100.

You could also refer offsets back to the output and you would see that the more gain you have after an offset, the more significant it becomes as an error term.

If the 1st-stage gain is (say) 100 and, the 2nd-stage input offset voltage is (say) 10 mV, that offset voltage (when "referred" to the 1st-stage input) is 10 mV/100 = 0.1 mV. 

So, if the 1st-stage also has an offset of 1 mV, then the overall offset voltage (including the 2nd-stage referred offset) is 1.1 mV at the input terminals.

On the other hand, if the gain of the 1st-stage is 20, the 2nd-stage offset referred to the input is now 0.5 mV and, this much more significant than when the 1st-stage gain was 100.

You could also refer offsets to the output and you would see that with more gain after an offset, the more significant it becomes as an error term.