EDIT: Please disregard my post below. I just now saw/realized you are talking about “AoE1:DE”, and not AoE2:DE. I’ll leave my post here for posterity, though. As for AoE1:DE, I’m not sure if Multiplayer has a Classic Mode option, or not; sorry.
-=-=-=-=-=-The below is my response when I thought OP was talking about AoE2:DE -=-=-=-=-=-
Classic Mode as in, “old graphics and old audio”, or?
If that’s what you mean, you’re right, those things don’t exist in the packaged game. However, at least for audio, someone made a mod that you can download to have the old sounds/music back. I don’t know that a graphics mod has been created to do the same.
I also figured/assumed the game would have a “classic mode” or similar to be like the old HD or CD-ROM version of the game, and was surprised to find it’s not part of the game. It’s still a cool game, though.
If you don’t want the new Definitive Edition graphics/audio and don’t want to use mods, then you’d currently have to purchase/install AoE2:HD Edition.
However, please know there’s a big update coming within (probably) a couple weeks… as a one-year anniversary update for Definitive Edition. I’m hoping that they will put a classic mode in at that point. They haven’t said they will, but it’s just something I’m personally hoping they might do, and think it is entirely feasible they might. It would make sense to me. You know, let the DE version of the game shine exclusively for a year without distraction, but now one year later, give players the option to go retro/classic with audio and graphics, if they want.