For sequences of networks embedded in the unit cube \([0, 1]^m\), (weak) measure limits of sequences of empirical measures of vertex densities (vertexon functions) exist, and the associated (weak) measure limits of sequences of empirical measures of edge densities (graphexon functions) in \([0, 1]^{2m}\) exist, regardless of the sparsity or density of the limit graphs. This paper presents an extension of Graphon Mean Field Game (GMFG) theory to the vertexon-graphexon MFG set-up (denoted GXMFG). Specific second order dynamics are introduced for the inter-node influence mediated by the singular part of a network graphexon measure; this is analyzed in the particular cases of a network limit ring topology and a limit rectangular lattice topology. Existence and uniqueness results are presented for the corresponding GXMFG equations.