First of all, a large portion of that graph refers to methane not carbon dioxide. Methane has a half life of 10 years, as compared to carbon dioxide's thousands or tens of thousands.
Also take care to inspect, carefully, what these figures represent. This graph only counts transportation of final food product to stores under the "transportation" category: "Emissions from energy use in the transport of food items". In other words, the emissions from taking the packets of meat from a slaughterhouse to grocery store shelves. Not shipping loads of grain to ranches. The actual article [1] this image comes from explains this more clearly, "Food transport accounted for only 5% of this. This means that if we were to take the case where we assume a household sources all of their food locally, the maximum reduction in their footprint would be 5%". Transportation of feed to ranches is categorized under feed, not transportation.
This is why estimates for the amount of carbon emissions meat is responsible often vary by a large margin. Some place meat, alone, as responsible for 14-19% of emissions. Others place all food production (not just meat) as under 5%. It largely depends on whether you include things like transportation, nitrogen fixing via the haber process, and land conversion under the umbrella of food production or in their own separate categories.
1. https://ourworldindata.org/food-choice-vs-eating-local