We study and analyse a particular example of an interacting dark energy model with explicit dependence on the kinetic term of the scalar field, simply characterised by a power-law coupling function acting on dark matter only. The emergence of novel early-time scaling solutions in such scenarios enhances their theoretical interest by alleviating the coincidence problem, before the current period of accelerated expansion. A thorough analysis of the background evolution and linear scalar perturbations of the model pinpoints the signatures left by the coupling in the dark sector on the observables, namely the cosmic microwave background, lensing potential auto-correlation, and matter power spectra. A primary parameter estimation analysis, which incorporates data from cosmic microwave background temperature and polarisation, lensing, baryonic acoustic oscillations, and supernovae distance \textit{moduli}, reveals a non-vanishing prediction for the coupling strength between the dark sectors, encoded in the power-law parameter $\alpha$, bounded to the order of $10^{-4}$. While a model selection analysis using simple statistical indicators does not point to a preferred setting, a full Bayesian evidence study favours the standard $\Lambda$CDM model.