According to a10_5v4 - Arria 10 Hard Processor System Technical Reference Manual (2017.07.22), the EMAC of HPS supports the IEEE-1588 function.
Does this mean that, on this kit, the HPS's Ethernet port support the IEEE-1588 function?
If yes, because the datasheet of the Ethernet Phy KSZ9031RN connected to that EMAC doesn't mention the 1588 feature, does this mean that, the 1588 feature has nothing to do with the Ethernet Phy chip?
IEEE-1588 is at the EMAC level.
Have a look at the Arria 10 register map:
In the EMAC, at offset 0x700 you'll see the registers to implement IEEE-1588.