The problem is that gas production in the US hasn't increased, and therefore LNG is unable to make up for the reduction.
According to currently available news, the US is doing a good job in terms of gas delivery, and the fact that in the first 6 months of this year more was delivered than in the previous year shows that the US has serious intentions to fulfill its promises.
Through June of this year, the U.S exported about 57 bcm of gas as LNG with 39 bcm, or 68%, going to Europe, Refinitiv data shows. That is compared with 34 bcm, or 35%, of LNG exports shipped to Europe for all of 2021.
That means the United States has already sent more gas to Europe during the first six months of 2022 than it did in all 12 months of 2021. If exports to Europe continue at the same pace through the second half of 2022, the total increase over 2021 would be around 45 bcm.
The problem arose after the fire at Freeport LNG, which provides about 20% of the LNG capacity in the US, and that terminal will not be at full capacity until the end of the year.
However, it should be emphasized that the increased import of gas into the EU from the US causes a shortage of gas in some other markets that cannot (for now) compete with the prices that the EU pays for that gas.