atwoz, Pippy
The PC input may perhaps be an ordinary line in, which expects about 1Vrms, more if you want to saturate the ADC. Those line in connections are quite common on many motherboards and PCI(-e) audio cards.
A dynamic mic will have a signal output level of about -60dBV or even less. If the PC input is 1Vrms line in, then you may need 60-70 dB of gain to reach an acceptable level. Your current amp has about 61 dB of gain, max, so it might actually make sense if you need some more.
I had a very brief look at the MAX9814, and it appears to contain what we used to call a VOGAD: Voice Operated Gain Adjustment Device. If the AGC can be turned off, then the chip may be suitable, though I haven't read the whole datasheet yet.
If the AGC cannot be disabled, then I would be dubious about whether it would work for singing. Usually you would want a manual, variable gain amp for mic volume control, but not an automatic one. That could end up sounding extremely unnatural, as the pre amp would - intentionally - remove much of the dynamic power in the voice of the singer.
How bad this might be would depend on the actual delays involved, though.