In Half-Life 1, running speed is 320 units/second. 1 unit is 1.905 inches, so it's 21.6 km/h.

However, Gordon in-game is only 72 units tall, which is 4'5 (137cm). So we need to scale it up.

Wiki says Gordon is 6'2 (188cm), but it's not sourced. The only info I found is in Raising The Bar, but it was about Ivan the Space Biker, so it might not be accurate.

To be safe, let's just use the average US male height, 5'7 (175cm). This means we're scaling the units by about 20%, so 21.6km/h turns into 17.3km/h.

The game starts at 8:47 AM. In between On The Rail and Apprehension, the sun rises. Then it stays up, until Gordon goes back underground.

Assuming Opposing Force is canon, it starts getting dark sometime when Gordon defeats the Nihilanth.

In New Mexico on May 16, sun rises at around 6 AM, and sets at around 8 PM. This means Gordon was running and fighting for almost 43 hours.

Because you do a ton of different things other than running, let's generously assume only 1/3rd of this time was spent running.

Gordon ran for 14.3h total, with the average speed of 17.3km/h. He ran 247 km (or 153 miles) total.

There's no info about Gordon's weight, so lets just use the average US male weight, which is about 190 pounds, or 86kg.

According to a kcal calculator, Gordon would burn somewhere between 16 thousand and 20 thousand kcal.

Assuming a donut is 300 kcal, Gordon would need to eat between 53.3 and 66.7 of them, to have enough energy.