How significant is achieving electronic transport in a single qubit at room temperature?

First of all, electron transport in nanotechnology is nothing new. For example, Nitzan and Ratner wrote a review paper on electronic transport in molecular wires in 2003, and Google Scholar says that review paper has 2631 citations at the time of me writing this answer.

Electron transport (even at room temperature!) is fundamental to the mechanism of photosynthesis and cellular respiration, as most people will know if they have taken high school biology classes. So most people working in the area of artificial photosynthesis, will have seen room-temperature demonstrations of electron transport, even in human-made and lab-controlled artificial systems. There was a review paper written on this subject in 2013.

So achieving electronic transport at room temperature in a human-made and lab-controlled device, is nothing that the company mentioned in your question, has invented.

The only difference is that they did it in a "single qubit".
But what do they mean by "single qubit"?

I see nothing in the PDF that you gave us, that tells us even what type of qubits they are trying to make. Examples of "types" of qubits are superconducting qubits, nuclear spins (NMR quantum computing), qubits in ion traps, quantum dot excitons, electron spins (ESR or EPR quantum computing), photonic qubits, etc.

Since they are talking about "room temperature", we can rule out superconducting qubits. NMR-based quantum devices with many qubits, tend to operate at room temperature anyway, for example in this 4-qubit experiment that was done in 2012 , so a "single qubit" operating at room temperature and not having any quantum computing gates applied to it, is not impressive to me, if they're doing NMR-based quantum computing (here the challenge is in going beyond the 12 qubits which is the current maximum I've seen in an NMR-based quantum computer). ESR-based quantum computing is similar to NMR, and I don't see why "electron transport" is needed for any of the other types of qubits.

More generally:
Electron transport is not a requirement for quantum computing.

For example, the DiVincenzo criteria for making a quantum computer, do not say anything about needing electron transport.

"I am trying to assess the significance of electronic transport measurements being performed on a single qubit at room temperature, as claimed in the below press release: https://archerx.com.au/src/uploads/2021/02/20210222_Electronic-transport-in-a-single-qubit-achieved-ASX-Release.pdf"

That PDF unfortunately does not show every much at all. Now to be fair to them, for-profit companies often don't show the public a lot of detail about what they're doing, especially while their technology is still under development. The academic job market is extremely competitive, and sometimes is not fair, which means that a lot of very talented people with science training turn to starting a company and seeking venture capital funding to continue doing science, rather than getting funded through the university system, but the private investors providing the funds will want money to eventually return to them, and the chances of that happening are lowered if a competing company is able to know every detail about how the other company is building their technology since they can use that to put the same product on the market earlier. In universities, research grants are not expected to be "paid back" via future profits, and it's enough to publish a lot of papers that were made possible by the grant money, but more and more scientists are not getting the opportunity to access such research grants as long-term university jobs become less and less available.

So I don't want to be unfair to the company you mentioned in your question. At the same time, "achieving room-temperature electron transport in a single qubit" is not relevant for the most popular type of quantum computing right now (which uses superconducting qubits), not impressive in the context of NMR-based or ESR-based quantum computing (where room-temperature quantum computations have been done with several qubits, since many years ago), and unnecessary in most other types of qubits.

Near the end of the PDF in your question, they cite this paper on which the second author is the CEO of the company in question. This is the only paper by anyone related to the company, which is actually cited in the PDF, and it's from 5 years ago, and it has had an unfortunately low number of citations despite being published in Nature Communications. This indicates that the work has not managed to penetrate the interest of the broader scientific community. The end of the abstract says:

"These results demonstrate the feasibility of operating electron spins in conducting carbon nanospheres as quantum bits at room-temperature."

Maybe 5 years later when the PDF in your question was written, they were referring to this "feasibility" now turning into "reality", meaning that they managed to make one qubit using electron spins in conducting carbon nanospheres at room temperature.

Considering that every single company listed here has already made devices with at least a couple dozen qubits, the single-qubit result at room temperature seems to be years or decades away from turning into anything competitive with what already exists on the market.

Finally: People often hear "milli-Kelvin" and think "wow quantum computers require extremely low temperatures, that's bad". But the dilution fridge required for helium-based cooling of qubits in D-Wave, Google, IBM, Rigetti and most other companies that make quantum hardware, is not really very expensive (compared to everything else) nor "extreme" in this field. Not only do techniques like "laser cooling" and "evaporative cooling" help several labs around the world reach nano-Kelvin, pico-Kelvin, and even negative temperatures (so the milli-Kelvin temperatures of D-Wave's hardware, for example, are not actually "extreme"), working at low temperatures can be a good thing in quantum computing. Decoherence rates will be much lower. Sure the company mentioned in your question might be able to (sometime in the future!) make a device with more than just one qubit, but if their goal is to work at room temperature, then I worry that decoherence could be a major problem. If they show us the decoherence times for their qubit at room-temperature, and show us that it's possible to apply 2-qubit gates and connect together dozens of qubits, then it might be something worth looking at in more detail, but they seem to be years or decades away from that.