I've read the stories about the EW pipeline posited as the main reason in another answer, but that to me seems ancillary to the main dispute, which was about gas pricing.
Essentially, Russia didn't need/want the EW pipeline in 2008 anymore because it had decided to substantially reduce gas imports from Turkmenistan. The latter came about due to a combination of reduced demand due to the global recession and Turkmen insistence on the (recently raised) price. RFERL reported (in another story):
In 2007, with world gas prices on the rise, Russia had promised to pay "European prices" to Kazakhstan, Uzbekistan, and Turkmenistan for their gas.
In 2008, Turkmenistan sold gas to two countries: Russia, via Soviet-era pipelines; and Iran, via a pipeline completed in 1997. That year, Turkmenistan sold some 40 billion cubic meters (bcm) to Russia -- and there were negotiations to boost that by another 5-8 bcm -- and 5-6 bcm to Iran.
[...] Additionally, construction was well under way on new gas pipelines leading from Turkmenistan to China and Turkmenistan to Iran, respectively.
Gas prices dropped during 2008. The Russian daily Vremya Novostei reported in April 2009 that Gazprom had lost more than $1 billion purchasing Central Asian gas in the first quarter. Kazakhstan and Uzbekistan agreed to lower their prices; Turkmenistan did not. And when the explosion hit the gas pipeline on April 9, 2009, Turkmenistan's government complained loudly that it was Russia's fault.
The result was a halt in Turkmen gas exports to Russia. When, in 2011, the two sides finally agreed on a resumption of supplies, and the pipeline was repaired, Russia said it would take no more than 11 bcm per year.
So yeah, the relationship (and the pipeline) was repaired, but at a quarter of the old volume.
Jamestown Foundation wrote (in late 2009) in slightly more detail about the timing of the dispute:
Less than two years ago, in March 2008, Russia agreed to raise the gas price for Turkmenistan, Kazakhstan and Uzbekistan up to European levels from 2009. As a result, Gazprom had to buy Turkmenistan’s gas well above the domestic cost. On June 1, Gazprom deputy CEO Valery Golubev urged Turkmenistan to either cut its export volumes to Russia, or scale down gas prices. He argued that Gazprom no longer needed Turkmenistan’s gas at European prices as European and Ukrainian gas consumption plunged (Interfax, June 2). Golubev also claimed that Ashgabat had no alternatives but to sell its gas to Gazprom. However, the Turkmenistan-China gas pipeline project came as an indication that Ashgabat managed to develop alternative gas export routes. [...]
During the first quarter of 2009, the sharp drop in energy prices cost Gazprom over $1 billion on gas purchased from Central Asia and resold at a loss in Europe. While Kazakhstan and Uzbekistan agreed to lower their prices, Turkmenistan refused. The saving grace arrived in early April, when a mysterious explosion close to the Turkmen-Uzbek border shut down the CAC-4 pipeline, halting nearly all exports of Turkmen gas.
As for the EW pipeline, essentially Ashgabat decided to switch it from Russia's Caspian pipelines to the [then] hoped-for Nabucco, but this was essentially because they were hoping to sell directly to Europe, at the higher prices. Interestingly, perhaps, they continued to build that EW pipeline, even when no interconnect to Europe or Russia was on the horizon anymore:
Russia was well ahead of this
competition primarily because it had already signed an
agreement with Turkmenistan in April 2003, in which the
former would import 2 trillion cubic meters (Tcm) from the
latter over the following 25 years. The gas trade between
these two states was expected to rise significantly, from 5–7
billion cubic meters (Bcm) in 2003–2006 to 70–80 Bcm by
2009 [...]. Therefore, Russia needed to expand
the capacity of the existing Central Asia–Center (CAC)
pipeline and build a new pipeline. This new pipeline was
the Caspian Coastal pipeline, which would run in parallel
with the western branch of the CAC (CAC-3) from
Turkmenistan’s western coast toward its final destination
of Russia after crossing Kazakhstan. In May 2007, the
presidents of these three countries signed a framework
agreement to build the Caspian Coastal pipeline [...]. Against this backdrop, Russia saw the need to transport
gas produced in the eastern part of Turkmenistan to the
western part in order to feed into this proposed pipeline.
Thus the EW pipeline project was born. Obviously, Russia
planned to connect this pipeline to the Caspian Coastal
pipeline. However, the 2008 global financial crisis dramatically
changed the situation. Gas demand greatly decreased
and Russia developed a gas surplus, which removed its need
to import gas from Turkmenistan and damaged the Russian
Turkmenistan’s intent became clear at a news conference
held during the tenth summit of Turkic-speaking countries
in September 2010. There, Berdymukhamedov explicitly
stated that the EW pipeline was closely related to the
Nabucco gas pipeline [...]. Turkmenistan’s Foreign Ministry explained why the country
needed to export its gas to Europe while heavily criticizing
Russia’s then–deputy premier Igor Sechin’s comment that
“Nabucco has no future” (RIA Novosti 2010). [...] Turkmenistan continued to build the EW pipeline despite
the fact that no concrete progress was made in connecting it
to any export route heading toward Europe. [...] Ashgabat completed
building the remaining part of the pipeline only six
months behind the original schedule.
This is a bit beyond my Q, but there was a 2nd pricing dispute in 2016, which again resulted in a complete halt of Turkmenistan-Russia gas shipments, and then
Russia's state-owned energy giant Gazprom resumed the purchases of Turkmen gas in 2019 when it signed a five-year contract envisaging annual deliveries of 5.5 billion cubic meters.
This volume was again down compared even to the to 2011-agred one. While Turkmenistan nowadays seems to bet on doubling exports to China (to 70 bcm by 2030). So, yeah, "destroyed" may be an overstatement when it comes to Turkmenistan-Russia gas exports, but they seemed to be trending down since 2008. After every pricing dispute [and a temporary complete halt], the contracted quantity with Gazprom appears to have gone down. OTOH, the actual export volume to Russia was up to 10 bcm by 2021, over the  contracted minimum. FWTW, I found this graph with exports by destination, but it is a bit misleading as to the present state of affairs, because it stops in 2018. OTOH, the piece quoted in my Q was written in 2018 too.
N.B. the [recent] increase was announced in Dec 2021 over 2020 volumes:
Ambassador Alexander Blokhin said Russia this year  stands to import about 10 billion cubic meters (353 billion cubic feet) of gas from Turkmenistan, nearly twice the amount imported in 2020.
According to TASS, quoting the same ambassador, the volume was back to 5 bcm in 2022 though (i.e. 2019 level).
As far as "hope for the best" pipeline building goes, apparently Turkmenistan has also began construction of a pipeline towards India, even though this has to cross (the [now] Taliban-controlled) Afghanistan. The Taliban promised at one point (in 2021) they'll let the pipeline be built, but I've not seem more recent news.