The caliber designation of 7mm-08 is considered a short action.
A Remington Model 700 chambered for the 7mm 08 cartridge would be a short action as the cartridge is based on the .308 Win.
The start of long action cartridges is the 30-06. The 7mm Mag is longer than 30-06, so would it be considered long action.
Long
The 7mm Mauser is generally considered short action. 7x57 is shorter than 30-06. OTHER 7mms are different lengths.
.308, and its derivative cartridges (like .243 and 7mm-08) and generally short actions. 30-06 at its derivatives (like 270, 25-06) are long actions.
17 Remington, 220 Swift, 222 Remington, 223 Remington (5.56mm), 22-250 Remington, 243 Winchester, 257 Roberts, 308 Winchester (7.62mm), 7mm-08.
NO!!
A while back there was a long action version of the Savage Model 12 (I think it was the 112BVSS) that was chambered in 7mm Remington Magnum. The last I ever really heard of them was back in the late 1990s. I've not seen anything about it since then. For now the only manufacturer that makes a bull barrel 7mm Remington Magnum is Remington, their Sendero line, as a matter of fact.
Ruger American Rifle short action calibers (.243 Win, .308 Win, 7mm .08 Rem, 22-250)
long action: 270, 30-06, 7mm rem mag. Short action: 243, 308, 7-08, 7mm wsm.
284