We can see things moving faster than light

Thank you! This is a decent explanation why the Hubble sphere is NOT a horizon, although you could have used a slightly more accurate figure of 14.5Gly (z=1.48). 

However, @11:12 Gravity does NOT overcome the expansion of space. There is not tug-of-war between gravity and expansion. Space simply does NOT expand where it is curved (described by a metric other than the FLRW). The cosmological constant (expansion) is contained only in the FLRW metric which describes flat spacetime.