tl;dr It wasn't really his ship that did it, it was him; given his 'God-Mode' powers.
Well, Ego is a supremely powerful being, he's actually a Celestial. In a sense Ego has "IDDQD" or 'God-Mode' abilities with a bit of "IDKFA" mixed-in. As he explains to the Guardians, it seems to just be a thing that he can do:
Gamora: You destroyed 1000 ships without even a suit, who can do that?
Ego: I'm what's known as a Celestial, sweetheart
Peter: Wait, a Celestial? As in a God?
Ego: With a small "g". At least on the days I have the modesty of Drax.
-Guardians of the Galaxy: Vol. 2. [paraphrased]
It seems to me that it's not really his ship that can do that, rather it's him. In fact, everything he has - his ship, his planet, his physical body - is in fact him, or rather a manifestation and extension of his self.
If you recall, in the scene where Ego destroys the Sovereign fleet, Ego is actually seen standing atop his ship, straddling it like some sort of steed, with harnesses and everything. It's not clear where the white blast type attack comes from, but his dialogue with Gamora seems to suggest that it was him that did the damage, not the ship.
In fact, in subsequent scenes, when Ego utilises his "power", he is seen doing so without any aides or weapons; as does
Peter, once he realises his potential too.
Skynet is the virus
Or rather, Ego is the ship.
This is where it gets tricky: Ego is based on the comics, however it is not a verbatim adaptation. Ego seems to have some extended abilities; namely his physical 'human-like' form and other extensions - such as his ship. Additionally, Ego from the movie is said to be a Celestial, whereas the comics version is not.
This is why, apart from the information we're given in the movie and any additional information given to us via the creators, it's not possible to give more insight about his ship or other abilities.
However, from what we can see, his ship:
- Can travel at FTL speeds
- Doesn't seem to require the use of "jumps" to travel from Berhert (the planet that the Guardians crash-land on after the Sovereign attack) to Ego's Planet
- Looks like an egg
- Can transport people within it (duh)
- Can transform its shape
- To create an opening as a door
- To create a moving platform which acts as a travelator