We report directional point-contact spectroscopy data on the novel Bi2Te3/Fe1+yTe interfacial superconductor for a Bi2Te3 thickness of 9 quintuple layers, bonded by van der Waals epitaxy to a Fe1+yTe film at an atomically sharp interface. Our data show a very large superconducting twin-gap structure with an energy scale exceeding that of bulk FeSe or FeSe1-xTex by a factor of 4. While the larger gap is isotropic and attributed to a thin FeTe layer in proximity of the interface, the smaller gap has a pronounced anisotropy and is associated with proximity-induced superconductivity in the topological insulator Bi2Te3. Zero resistance is lost above 8 K, but superconducting fluctuations are visible up to at least 12 K and the large gap is replaced by a pseudogap that persists up to 40 K. The spectra show a pronounced zero-bias conductance peak in the superconducting state, which may be a signature of an unconventional pairing mechanism.