Finally my demographics class can prove itself useful! Unfortunately, that's not how several things work.
A mortality rate refers to the number of deaths *in one specific year* divided by the population in the midpoint of that span (generally July 1st in calendar years, even though it's not the midpoint of the year). So, it is expected that in a population with the characteristics of 2004 USA (the data360.org set), we can assume that 900 deaths of 55-59 year old males will come from a population of 100,000 55-59 year old males in the next year.
Contrast that to a risk of death, which is the number of deaths coming from a population in one year divided by the total population at the *start* of that year. Said population is usually sex- and age-specific.
I'm afraid your 13.6% figure isn't a mortality rate at all, nor is the population it concerns "55- to 65-year-old males". It is the estimator of the cumulative risk of death for an Aki 1984 sekitori from 1985-2019. To approximately compare it with the contrasting figure for the American population, you have to take the product of the complements for the risks of death that match the ages of the sekitori in question for each year (e. g., one minus risk of death for 28-year-old males in 1985 multiplied by one minus risk of death for 29-year-old males in 1986, etc until 2019), and then subtract the whole thing from 1.