No Enigma isn't a privacy coin in that sense. It's private computation, more like smart contracts which are private, more like Ethereum with private computation than Bitcoin.

What Enigma in theory could do is allow people to identify themselves to the network without putting themselves at risk for being accused of being involved in the dark markets. The network would simply compute your identity with a smart contract and could in theory show you did nothing wrong without violating your privacy in the process. This would allow you to minimize your risk of exposure to law enforcement, tax authorities, etc.

If you are trying to take risks, and willing to risk jail to be involved in dark markets, I don't think Enigma has any advantage over Zcash or Monero for that. The advantage of Enigma is it would allow stuff like KYC in a completely private manner without any particular human beings knowing the identity. Think of it as a trustless KYC which could be possible where the computation could for example verify that your passport is legitimate and your address is legit, without some human somewhere being able to connect your pseudo-anon identity to your flesh and blood.

That to me is enough of a privacy gain for what I do. Pseudo-anon yet also verified as a flesh and blood person? That for many is a holy grail for free speech and for business as it will make it safer to do business. Any information which you want to share without having it linked to your real world identity would benefit from homomorphic encryption and any information which you want to submit for analysis while redacting the parts dangerous to your interests is also possible with homomorphic encryption.

So for protecting yourself from law enforcement if you are an honest actor, you will want a way to prove you are an honest actor without putting your privacy at risk (hackers, the crowd, and others who want to collect info). The network would let you prove honesty (proof of honesty?) and this in my opinion could allow law enforcement to in a sense rule out many in their investigation.

Take for example the IRS which for instance is digging into Coinbase? The IRS wanted to say all users of Coinbase are somehow tax cheats. The search was narrowed down by a judge (good decision in my opinion) only to people who were trading over $20,000 over a calender year. Using homomorphic encryption, using Enigma, it would be possible for a user to prove their total trades under the accounts linked to their identity, are less than $20,000 per year. This in fact is the millionaire's problem and has been solved specifically by secure multiparty computation. It is also possible to use this secure mechanism of computation to allow an account holder to prove they are a sophisticated investor (millionaire).

References

Lin, H. Y., & Tzeng, W. G. (2005, June). An efficient solution to the millionaires' problem based on homomorphic encryption. In ACNS (Vol. 5, pp. 456-466).