Do I need to host Azure ATP (Defender for Identity) in my own servers?

Sal_Mirza 
The equivalent of the "Center" machine is now a hosted service managed by Microsoft, so You don't need this machine any more.

The Equivalent if the "Gateways" is now called "Sensors", and those are replacing the Gateways, still installed on your machines, only in MDI, the best practice is to install them on the DC itself  and not as a standalone machine with port mirroring, as  this way we get more data sources from the machine and doing much better detection.
Also, MDI supports multi forest, so in case you had to work with multiple Center machines before, you don't need that any more and can get full/better coverage with a single MDI tenant.