Even small 1 hp electrical motors can achieve that RPM
Yes, but can it sustain that RPM when something tries to stop it, that is the question. 1 hp combustion engines can get to 2700 rpm as well, but you cannot attach a propeller to it, stick it in the air, and expect it to maintain the RPM. It takes a lot of torque to create aerodynamic thrust.
It is a fact that electric motors are way better at producing torque than combustion engines. An electric motor produces almost maximum torque at the get-go, with the rotor standing still. The combustion engine needs to make RPM in order to make torque. This article compares electric motors with combustion engines for powering a hydraulic pump: a 20 hp electric motor can do the job that a 50 hp combustion engine can do.
Combustion engine: intermittent torque means torque pulse from combustion.
But wait, is that even possible? Power is power, kilowatt is kilowatt, and it should not matter which engine we use to generate the kilowatts, they should all equate to equal amounts says the first law of thermodynamics, the conservation of energy. But it does matter, since with a combustion engine torque is a function of RPM. So increase RPM, and power increases due to increased RPM and increased torque. At lower RPM the combustion engine may simply lack the torque to speed up, while the electric motor has an almost flat torque curve.
This same happens with outboard motors, when comparing 2-stroke with 4-stroke. 2-stroke has way more torque at lower revs, the 4-stroke may have the same horsepower but may never get to the high revs because it lacks the ability to get the boat planing.
But I digress. To get back to your questions:
What's the use of so much torque, and what happens if there is less torque at the same RPM
To keep the output shaft at this RPM while the propeller is pushing all that air backwards. That requires a serious amount of torque. If there is less torque at the same RPM, there will be less thrust produced and the aeroplane won't fly as fast.
Can an electric motor perform similar to the Lycoming IO-360 with the same max. RPM, but with just half the torque of the latter?
Well, the surprising thing is that a horsepower is not a horsepower. Part of the problem lies in the horsepower output functions, so maybe an electric motor with a lower hp rating can be used. But one thing is very clear: at the RPM of the propeller, a certain torque is required at a certain speed to keep the propeller turning. This amount of torque will always be the same, no matter what kind of engine produces it.