To quantify the role of radio jets for Intra-Night Optical Variability (INOV) in Radio-Loud Narrow-Line Seyfert 1 (RLNLSy1) galaxies, we report the first systematic comparative INOV study of 23 RLNLSy1 galaxies, with 15 RLNLSy1s having confirmed detection of jets (jetted) and the remaining 8 RLNLSy1s having no detection of jets (non-jetted) based on their Very Long Baseline Array observations. We have monitored these two samples, respectively, in 37 and 16 sessions of a minimum 3-hour duration each. Based upon Fη-test at 99% confidence level with a typical INOV amplitude (ψ) detection threshold of > 3%, we find the INOV duty cycles of 12% for the sample of jetted RLNLSy1s, however, none of the sources showed INOV in the sample of non-jetted RLNLSy1s. Among the jetted RLNLSy1s, we find that the Duty Cycle (DC) for jetted γ-ray detected (γ-ray) RLNLSy1s is found to be 34% in contrast to null INOV detection in the case of non-γ-ray RLNLSy1s. It suggests that instead of the mere presence of a jet, relativistic beaming plays a significant role for INOV in the case of low-luminous high accreting AGNs such as NLSy1s in which dilution of the AGN’s non-thermal optical emission by the (much steadier) optical emission contributed by the nuclear accretion disc is quite likely. Our study of jetted γ-ray RLNLSy1s shows more frequent INOV detection for sources with higher apparent jet speed. Further, our results also suggest that among the NLSy1s, only jetted γ-ray RNLSy1 galaxies DC approaches blazar like DC.