James Tabiri, 57, was working as a sort line operative at Biffa Waste Services' waste transfer site on Peace Street when he was struck on 10 August 2023.
A Health and Safety Executive (HSE) investigation found the company failed to "effectively review and monitor" the measures in place to "protect pedestrians" and keep them away from moving vehicles.
The company was fined £2.48m and ordered to pay further costs of £5,768 at Leeds Magistrates' Court on Wednesday, according to the HSE.
Biffa Waste Services Ltd, of High Wycombe, Buckinghamshire, earlier admitted breaching Regulation 5(1) of the Management of Health and Safety at Work Regulations 1999.
CCTV footage from the previous week showed that it was "common practice" for workers to bypass segregated pedestrian routes, the HSE said.
Some were seen climbing over barriers intended to keep them safe, a spokesperson added.
His inquest heard that Mr Tabiri had left the canteen and walked through the site wearing an orange hi-vis jacket before he was hit.
Elliot Archer, HSE inspector, described the incident as "easily avoidable".
"Control measures were in place to allow pedestrians and vehicles to move safely, but a lack of monitoring and supervision allowed poor working practices to develop between the workers on site," he said.
"Our investigation found a casual attitude to health and safety, with workers treating a high hazard site like a playground."
Gary Carvell, Biffa's health and safety director, said: "On behalf of the company, I wish to extend my deepest sympathies to the family, friends and colleagues of Mr Tabiri.
"We recognise in this case that the arrangements in place to ensure the safe separation of pedestrians and vehicles were not effective and we accept full responsibility for the breaches accepted in court.
"Immediately following the incident, we carried out a comprehensive health and safety review of the site and made several changes to reduce the likelihood of further harm. We are committed to workplace safety across all our UK sites."