Based on provisional data, yes, the death rate among vaccine recipients is much lower than that of non-recipients. But this kind of raw comparison leaves out important details, as I'll mention at the end of this post.
It's not too hard to run the numbers here. Your quote says that from 2020/12/14 through 2021/03/15, there were 1913 deaths. I went to this CDC page which gives (provisional!) weekly death counts from all causes. I selected the weeks ending 2020/12/19 through 2020/12/13 as this is the closest to matching the date range you gave. Adding up the weekly totals gives a total of 843,804 deaths from all causes over that time period. Subtracting the 1913 vaccine-recipient deaths leaves 841,891 deaths that we assume were among those who did not receive the vaccine.
This other CDC page tracks the number of people who received a COVID-19 vaccine. According to that, 79,367,225 people have received at least one dose of vaccine. (Note this is less than the 109 million you quoted, as some people received two doses.) If we estimate US population at 330 million, that means the other 250,632,775 have not received a vaccine.
Thus the death rate among vaccine recipients is
1913 / 79367225 or (scaling for easier-to-interpret numbers) about 2.4 deaths per 100,000 people. The death rate among non-recipients is
841891 / 250632775 or about 335.9 deaths per 100,000.
Of course, there's a lot of sloppiness in these calculations. The date ranges do not correspond exactly, and even if they did, it's difficult to find reliable data on deaths up to such a recent date. There were almost surely deaths before March 13 which are not yet represented in the CDC data for various reasons. (That's why the CDC page lists provisional death counts.) The same is true of vaccine totals. And of course the value used for the total US population is just a very rough estimate.
Also, although I don't have data on this, I would be especially suspicious of the vaccinated death count given by the CDC. As noted on that page, that death count is based on reports submitted to VAERS, which tracks adverse events. Healthcare providers are required to report deaths of vaccinated individuals. However, due to the rapid, varying, and often chaotic rollout of the vaccine, record-keeping may lag, I could easily imagine that there are people who were vaccinated and then died without their death being flagged as a death of a vaccinated person, let alone reported as such to VAERS. This would mean that the death would be included in the total of all deaths but not in the total of vaccinated deaths. (For instance, I received my first dose of the vaccine three days ago; no one has a record of this except the pharmacy where I got it. At some point they may transmit that to my insurance company or somewhere else, but if I happen to get hit by a bus next week I have serious doubt that my vaccination record would be linked up with that, at least not for some time.)
As I mentioned at the beginning, though, this whole calculation is an extremely coarse way of looking at the vaccine. We are dividing the entire US population into only four groups, based on whether they are dead or alive and whether or not they received a COVID vaccine. The populations that were vaccinated first included disparate groups with wildly different mortality patterns. The benefit in reduced death rate may be even larger among the elderly, who are at high risk of death from COVID if infected; on the other hand, the figures for total deaths and total population include children under 16, who cannot yet even receive the vaccine.
Over the time period in question about a quarter of all deaths in the US "involved COVID-19" according to the CDC. The death rates above are broadly consistent with the idea that the vaccine is reducing the death rate due to COVID, but I wouldn't want to read too much into them.