It was a journey at high speed through the desert – in a pick-up truck with armed fighters in the back. We were travelling with Yemen’s pro-government forces, catching glimpses of the Arabian Sea, and forbidding mountain peaks in the distance. Houthi rebels were dislodged from here just days ago, we were told.

When you are battling over expanses of empty desert, progress can be hard to see. But these soldiers, in Shaab-al-Jinn in Lahj governorate, showed us new sandbagged defences – new lines in the sand.

“There was heavy fighting,” said Tawfiq Al Haboun, a bearded commander in camouflage uniform.

“They have snipers, artillery and ballistic missile launchers.”

Here in the far corners of the Middle East, a war is being waged with global implications.

Yemen’s entrenched civil war is now impossible to ignore. It’s part of wider conflict, stretching from Tehran to Riyadh, where missiles slammed into the international airport this weekend. Yemen’s Houthi fighters – already a threat to global shipping – are an increasing threat to Saudi Arabia. And they provide leverage for their backers in Iran, Saudi’s regional rival.

Tawfiq Al Haboun pointed to shards of fibre glass and bits of metal at his feet – part of a downed Houthi drone that he said was carrying C4 explosives.

Commander Al Haboun is from the Southern Forces, part of the loose – very loose – alliance of groups fighting for Yemen’s government, which is internationally recognised, and backed by Saudi Arabia and its air strikes.

The Houthis swept into the capital, Sanaa, in 2014, ousting the government. A year later a Saudi-led coalition of Arab states intervened, trying to dislodge the Houthis. Despite years of devastating air strikes, that hasn’t worked.

The commander tells us about 500 Houthi fighters remain on high ground overlooking a strategic maritime corridor – Bab al-Mandab – connecting the Red Sea to the Gulf of Aden.

The narrow waterway, which is crucial for oil exports, was just out of sight on our trip.

The Houthis seized the area after a lighting advance in September. The commander claims pro-government forces have wrested back about 85% (the Houthis have denied losing territory in other areas but not here, as far as our local sources know).

Until they regain complete control, there will be pressure on global oil supplies and on prices.

We heard later that there were heavy clashes the day of our visit. Five military vehicles apparently hit improvised explosive devices planted by the Houthis. It’s unclear how many fighters were killed or injured.

As jitters run through international energy markets, hunger menaces weary Yemenis forced to flee this latest spasm of violence.

Around 200,000 have been driven from their homes since the start of this escalation at the beginning of September, according to the International Organization for Migration – all this in the Arab world’s poorest country.

As we left the area, we saw a tableau of suffering with families dotted around seeking shelter under scrawny trees. Among one group of women and children we met Aisha, gaunt and elderly and sitting on the ground.

“We have been here for 30 days,” she told me.

“I have no animals, no money, no water, no food, not even a blanket. And I am scared of the [Saudi] air strikes. We had to run, with just the clothes on our backs.”

At the weekend it was Saudi civilians at the international airport in Riyadh who were doing the running. The Houthi attack – the deadliest on Saudi soil in more than a decade – sent shockwaves around the region and punctured the kingdom’s sense of security.

But in operating rooms in Yemen’s port city of Aden, geopolitics feels remote. Hospitals are overstretched and doctors are working night and day to treat wounded government fighters coming from the front lines.

We visited one military hospital where 51 casualties arrived in a single day – many with gunshot wounds, and several needing amputations.

In a crowded ward, a Houthi fighter lay alongside fighters from the other side. Doctors tell us they make no distinctions.

“I don’t care where he comes from, his background or his religion. He is a human being so I should treat him as a human being, “said Dr Bassam Hazar.

Even if the war ends, some will never leave it behind. One man was sitting silently on his bed, a white bandage wrapped around the stump of his left arm, and staples running along his crown.

Others have not lost their fighting spirit, like Ahmed Ali Mahmoud who is smiling and animated, despite multiple fractures.

“I am not waiting to be fully recovered,” he tells us.

“I just want to be able to stand. I think it is a religious duty and a national duty [to go back to fight]. The Houthis have destroyed the country. With victory I won’t even feel these fractures.”

In the next ward lies 12-year-old Ali, a brown-haired boy, who is just one year older than Yemen’s civil war. Ali was injured by a drone as he walked down the street and is facing a complicated surgery.

“There is shrapnel near his spine,” says Dr Amr Reyadh Assaqaf, standing by his bedside.

“The operation won’t be easy, but God willing our staff will be able to handle it.”

He tells me Ali is quiet and gentle.

“At first he was depressed,” he says, “but we gave him toys to play with and his mood is gradually lifting.”

But will war follow him into adulthood?

A truce in 2022 brought a few years of relative calm. But now the Houthis are a stronger enemy, as they have proven at the weekend. They already control most of Yemen’s population. If there is a new attempt at mediation – and there is some speculation about this – they may drive a hard bargain.

Back at the hospital, as he prepares for the next wave of casualties, Dr Bassam Hazar hopes for change but doesn’t expect it soon.

“Maybe war is good for news,” he says, “but it’s horrible [for people].

“Sons are losing their fathers, and mothers losing their sons. We need peace.”

Additional reporting by Wietske Burema, Lee Durant and Suaad Al Salahi