The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infected about 1.5 billion people in our world, causing critical public health concern and over 7.5 million deaths due to its associated disease, the coronavirus disease 2019 (COVID-19), to date. COVID-19, specially severe cases, is characterized by increased proinflammatory-cytokine production and worsened lung inflammation. In addition to antiviral drugs, there is a requirement for antiinflammatory medications to act against all or most phases of COVID-19 and its cytokine storm. One of the most attractive therapeutic targets for COVID-19 is the SARS-CoV-2 RNA-dependent RNA polymerase (RdRp), an enzyme essential for viral replication. RdRp inhibitors, therefore, have the potential to halt viral replication and work as antiviral therapies. Since a number of kinase inhibitors are known to successfully work in inflammatory pathways, this could also be looked into as a possible antiinflammatory treatment to effectively cool COVID-19 through controlling its major severe and critical symptoms. Therefore, taken together, targeting SARS-CoV-2 RdRp with kinase inhibitors may be a potential approach for discovering compounds with dual activity (antiviral and antiinflammatory actions). Doramapimod (BIRB-796) is a kinase inhibitor known for its good antiinflammatory and immunomodulatory activities. As a representative of kinase inhibitors, this pyrazole derivative was selected to be computationally tested in the current study, using mainly molecular docking/dynamics simulations, due to its previously-demonstrated potent inhibitory activities against the coronaviral-2 main protease enzyme (Mpro), aiming to support its potential antiviral effect data against SARS-CoV-2. The current computational findings, particularly those pertaining to the relatively perfect hitting of the conserved regions of SARS-CoV-2 RdRp, significantly validated the earlier biochemical findings as well as the presently-proposed dual "antiviral-antiinflammatory" action, uncovering the anticipated integrative as well as broad-spectrum activities of doramapimod against COVID-19 and any future similar coronaviral diseases caused by any futurely-emerged sarbecoviruses/coronaviruses, e.g., SARS-CoV-3 and SARS-CoV-4.