What kind of op-amp circuit is this?
Which kind of category this circuit belongs? I guess it belongs to
differential amplifier type. Is it right?

No, it's a single-ended amplifier because it doesn't have the all important extra resistor that would connect the non-inverting input with the 1.65 volt DC supply rail. See added resistor in red below: -

That added resistor would make it a proper differential amplifier.

There is a voltage offset added at non-inverting input of the op-amp. If I remove this offset, the simulator shows simulation error. What's
the purpose of this DC input there?

Removing the offset (as in making that offset equal to 0 volts) will slightly alter the DC output from 1.65 volts to 0 volts. However, if you just removed the supply of 1.65 volts, then the non-inverting terminal wouldn't be biased and the output wouldn't be defined.

Can I get the same output without adding DC offset?

Make the DC offset 0 volts and you will get the output sinewave centred around 0 volts.
The use of two 560 kΩ resistors looks like a security measure to prevent the high voltage source (530 V RMS) from potentially injecting harmful currents into the op-amp. To understand this you'd need to consider the actual voltage source in the real circuit that the simulation is mimicking. It's likely to have several tens of pF capacitance to ground (or maybe hundreds of pF) and that leakage capacitance can form a loop that would produce excessive current into the op-amp should there not be 560 kΩ resistors present.