To achieve the strategic goal of carbon neutrality, optimizing the low-carbon operation of integrated energy systems (IES) through multi-energy coupling and synergy has emerged as a critical pathway for energy transition. Within the framework of multi-energy coupling and cooperative operation, a muti-dimensional optimal scheduling strategy incorporating multi-timescale analysis and load demand response is proposed. First, a multi-level coupled architecture for gas turbine-carbon capturing and storage-power to gas (GT-CCS-P2G) is constructed, and an integrated electricity-gas system (IEGS) considering comprehensive demand response is structured based on this architecture. Followed by the construction of the power grid and gas network as separate agents, and the conversion of the IEGS scheduling scheme into a Markov game process. Finally, the optimal scheduling strategy is obtained by the communication mechanism-enabled multi-agent soft actor-critic (CM-MASAC) method. Comparative analysis with multiple algorithms demonstrates both the superiority of the proposed method and the synergistic effectiveness of combining load demand response with GT-CCS-P2G technology. Experimental results indicate that this approach achieves optimal performance, reducing 10.29% operating costs and 16.07% carbon emissions compared to benchmark methods.