micronucleus VS HoodLoader2

You can actually bit-bang low speed USB on Arduino [0]. There is even a bootloader [1] for ATtiny. It is obviously not compatible with Arduino, but those tiny boards look too cute to ignore [2]. Also, you can use USB port both for downloading firmware and your application.

[0] https://github.com/obdev/v-usb

[1] https://github.com/micronucleus/micronucleus

[2] https://cpldcpu.wordpress.com/2014/04/25/the-nanite-85/

The Digispark[1] and its clones use the ATTINY85 and offer flashing over USB via the Micronucleus bootloader[2] using V-USB[3]. It comes at the cost of a significant chunk of flash storage, but the convenience is excellent. Plus, V-USB support means you can emulate all sorts of USB devices. I've used it to build a DIY NES controller adapter, but it's commonly used as a cheap Rubber Ducky[4]. For projects where USB interfacing makes sense, it can be a good fit.

1: http://digistump.com/products/1

2: https://github.com/micronucleus/micronucleus

3: https://www.obdev.at/products/vusb/index.html

4: https://shop.hak5.org/products/usb-rubber-ducky-deluxe

So it looks like they're using the micronucleus bootloader for the linked example. That bootloader not only does the normal bootloader job, but also acts as a bitbanging USB device in order to communicate with the computer over USB. The USB bitbanging is a huge endeavor to undertake on top of writing a bootloader.

The Mega2560 like the Uno has a second MCU that does the USB-Serial stuff, an atmega16u2. You can flash this one to show up as a USB HID device instead of serial through Hoodloader (https://github.com/NicoHood/HoodLoader2).

The library is compatible with all boards using the MCU ATmega32U4. This includes Arduino Leonardo, SparkFun Pro Micro, Arduino Micro, and Adafruit 32u4 AVR Boards. It also supports the Arduino Uno and Arduino Mega, but this requires the HoodLoader2 bootloader, see this wiki for more details.

hoodLoader2 might help you out. I've no experience with it though.

You should buy a Leonardo if you want to do USB projects, the Uno can do that stuff too - it has a small microcontroller (16u2) that's a cut down version of the one on the Leo (32u4) that handles the USB to serial conversion required for a PC to communicate with the main microcontroller (328P) on an Uno, the 16u2 can be reprogrammed to make the board appear to be anything - but it's harder to achieve for beginners. If you're interested in reading more, take a look at https://github.com/NicoHood/HoodLoader2, but if you just want to do keyboard and mouse stuff quickly with all "off the shelf" hardware and software (and the community support that entails) the Leo is definitely your best bet.