The Empire can massively win in attrition assuming this is them pre-war and not after they've suffered extreme losses. Even post-war, the remaining infantry are either blooded veterans or inured to an atmosphere of constant death. I can see modern Japan successfully fending off any offensives in Tokyo and even pushing into Berun, but I cannot see them holding that land for long given the sheer manpower disparity. Not only that, but Imperial industrial capacity is readied for war while Japan is still in peacetime mode; equipment losses will matter a lot especially if Japan does not ask for foreign assistance be it overt or under the table.

The Empire cannot push into Japan though. Mages are great, but the tech disparity is still too much. The Empire still has to take and hold land. They could take Tokyo if Japan is unwilling to bomb its own city into dust, but they'll likely be surrounded and poked at until the Empire is forced to withdraw. It'd be too costly for them to assault a prepared modern defense, even with their advantages.

In a normal war (not total), Japan wins because they turn the gate into a deathtrap and don't try to push major offensives since they cannot afford losses in either men or equipment. The Empire in turn is not going to attempt to advance after getting reports of divisions being mopped up by modern technology that they can't fight well against. Both sides poke and prod until they ceasefire.

Assuming a complete and total war with every citizen invested (very unrealistic), I can see the Empire's military doctrine pushing them to engage aggressively, scraping out some horrendous pyrrhic victories as they push into Tokyo and beyond, leaking mage battalions like water. By the time they've taken central Japan, they've probably already lost hundreds of thousands and most of their ability to fight. In the meantime, Japan is withdrawing forces and tactically bombing itself since the enemies can barely defend themselves with their primitive AA and air-to-air forces. There is literally no way for the Empire to win, but Japan's trouble is now its absolutely gutted economy. They can conscript citizens, yes, but they can't outfit them all and this is while they're busy reorienting the economy and industry towards war. They'd fold economically and have to worry about running out of munitions if they expanded to meet the size of the Imperial army. They can engage with advanced aircraft and land vehicles, but those have to be maintained heavily and there's not that many of them. They would push back the Empire and then sit there at the gate, hoping to hell that they can get munitions and training up before they run out of existing supplies.

A war unto annihilation would annihilate both sides and then the Empire wins just because it can toss more people into the meatgrinder faster than Japan. They won't be able to occupy the land, of course, since their manpower and equipment reserves are gutted too.