That mini-house thing IS recent. It is probably another small example of the Armenian Church thinking it can do (and being allowed to do) whatever it wants with the historical monumets it was given after the fall of the Soviet Union.
Photos taken in the 1970s show that there was a similarly-shaped structure at that same location in the building. But its pedimented roof was orientated in a different direction (north-south rather than east-west), and it had a miniature stone church at its apex, similar to the miniature churches that are at the apex of the gables of the main church. So, the original structure there has been entirely destroyed for some reason and has been replaced by something which does not match the original.
As for what it could have been, it may have just been an architectural solution to hide a messy join between the roofs of the church and the gavit. Or maybe it could have been an reliquary of some sort. If the latter is the case, perhaps its north-south orientation did not fit with the dogma of the current Armenian Church, so they had it destroyed and replaced with something more acceptable to them.
I think this is the same reasoning behind the destruction of that 19th century roof at Harichavank and its replacement with an historically inaccurate conical roof. Armenian Church dogma says that this is what an Armenian church must look like (steeply-pitched conical roof with a cross at its apex, raised floor level in the apse, etc.) and inconvenient examples showing that this has not always been the case, that the Armenian Church might have changed over the centuries, are removed.