An Explanatory Model for the Relationship between Motivation in Sport, Victimization, and Video Game Use in Schoolchildren

(1) Background: Society is changing amazingly fast, and this is bringing about changes in the way that people spend their free time. In the 21st century, free time is increasingly spent using technological devices such as video games, thus increasing levels of sedentariness. The aim of the present study was to define an explanatory model for the problematic use of video games, physical activity, motivational climate in sports, and victimization in schoolchildren, and to analyze the relationships between these variables according to gender; (2) Methods: A total of 734 schoolchildren, of both sexes, participated in this research study. They were aged from 10 to 12 and lived in the province of Granada (Spain). The main instruments used were the questionnaires PMCSQ-2, PAQ-C, QERV, and SVS. A multigroup structural equation model was used, which had an excellent fit (χ(2) = 319.472; df = 72; p < 0.001; CFI = 0.962; NFI = 0.952; IFI = 0.962; RMSEA = 0.048); (3) Results: The practice of physical activity was related negatively and indirectly to the problematic use of video games ((r = −0.085, boys); (r = −0.081, girls)), and this in turn was related positively and directly to victimization ((r = 0.094, boys); (r = 0.174, girls)). Additionally, task climate was inversely related to the problematic use of video games for girls (r = −0.133), and ego climate was directly related to the use of these devices only with regard to boys (r = 0.250). (4) Conclusions: It must be noted that schoolchildren’s pathological use of video games is closely related to lower levels of physical activity. In addition, those motivational climates in sports that are oriented towards performance exacerbate this pathological behavior, which accentuates the importance of promoting motivational climates that are oriented towards tasks in schoolchildren.