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As others have pointed out, the choice of the age range has a significant impact on the conclusions one is able to draw. In particular, this paper defines "Children and Adolescents" as 1 to 19 years old, which captures a lot of firearms related deaths due to gang violence.

Unfortunately, politics and culture war are infused in everything. But, if you want to be informed so that you can make better, persuasive arguments, I suggest looking at the CDC Child Health data here: https://www.cdc.gov/nchs/fastats/child-health.htm

TLDR: non-accidental deaths are weighted heavily towards 15-19 year olds, and due to that cohort's fraction of the 1-19 year population, when 15-19 year olds are lumped together with 1-14 yos, it allows someone to present data that homicides are the leading cause of death for 1 to 19 year olds. The further refinement from homicides -> firearms is presumably disambiguated in the referenced paper.

While the authors are obviously free to frame the data and discussion however they please, this strikes me as a paper designed to serve a policy position or perhaps guide political action more so than an even handed look at childhood deaths. Add to it the emotional impact that we're talking about children here, and I find it verging into the emotionally manipulative.

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CDC data

Children aged 1-4 years: https://wonder.cdc.gov/controller/saved/D158/D321F178

- Accidents (unintentional injuries); 8.5 deaths/100k

- Congenital malformations, deformations, and chromosomal abnormalities; 2.7/100k

- Assaults (homicide) - not broken down by assault weapon; 2.0/100k

Children aged 5-9 years: https://wonder.cdc.gov/controller/saved/D158/D321F179

- Accidents (unintentional injuries); 4.1/100k

- Cancer; 1.7/100k

- Assaults (homicide) - not broken down by assault weapon; 0.9/100k

Children aged 10-14 years: https://wonder.cdc.gov/controller/saved/D158/D321F180

- Accidents (unintentional injuries); 4.3/100k