It's not just the digestive tract. Our eyes, out lungs, even our skin rely on a huge diversity of specialized and symbiotic organisms to function correctly. This ecosystem evolved in parallel with our DNA, and it's been lost for the mammoth.
Yes, it seems we have the technology to create something with this DNA, but it won't be a mammoth as the organism existed in the past. It may not be viable, and it may suffer horribly.
Aside from that though, it may be important, but there are also lots of cross-species animals (ligers, mules, etc.) that don't get the full bacterial dose from the father of which half of their genetics come from and that doesn't seem to be a main cause of any of their problems that I've heard of.