Arduino UNO Rx/Tx speaks to itself
As Mikael Patel pointed out in his answer, you have set up a voltage divider. Mikael has thoughtfully provided a schematic of the clone Uno, where the relevant part is here:





Equivalent circuit

If you jumper together pins D0 and D1 (Rx and Tx) on the Uno effectively you have made this circuit:





Testing

If I set up this with a function generator, I get this result:



You can see that for a square-wave input of 0 to 5V, we only get an output of 2.16 to 5V.



What is LOW?

Now looking at the datasheet for the DC characteristics we see:



For an input to register as LOW it has to be no higher than 0.3 * Vcc = 0.3 * 5. Thus the voltage cannot be higher than 1.5V. Since we are measuring 2.16V, that will not count as a LOW.

Now admittedly that is for the Atmega328P and not the CH340G, but it will probably have similar characteristics.

I found a datasheet for the CH340G, and that shows even stricter requirements for a LOW signal:





Official Uno

Comparing to the official Uno circuit:



You will note there that the indicator LEDs are on a different circuit, and thus do not form a voltage divider.



The Maths

The clone Uno circuit above can be re-arranged like this:



Given that the LEDs have a voltage drop of 1.86V (measured in practice, and about right for the red LEDs I am using) then effectively we have the resistors R1 and R2 connected to 3.14V.

Since they are in parallel they are effectively 500 ohms.

Now using the formula for voltage dividers:

1000 / (1000 + 500) * (5 - 1.86) = 2.09V


This is close enough to the observed result. I didn't check each resistor to make sure it was exactly in spec.

I don't think R4 affects the results because it is effectively "floating".