Square Enix have released DRAGON QUEST I & II HD-2D Remake and you should be mostly good to go on Linux / SteamOS and Steam Deck with it.
Valve have stuck it with a Playable Steam Deck rating and it's SteamOS Compatible. The main issues noted being small text, plus it requires an internet connection for the first run and it doesn't default to external controllers - so you may need to use the SteamOS Quick Access menu to change the active controller.
Apart from that, you should be fine as everything else works with the testing being done on Proton 10.
Release trailer is below:

Direct Link
DRAGON QUEST I & II HD-2D Remake combines full remakes of DRAGON QUEST I and DRAGON QUEST II, which chronologically take place after DRAGON QUEST III HD-2D Remake which launched in November 2024. You will get to experience the conclusion to the Erdrick Trilogy in these two standalone epic adventures, with the upgraded HD-2D graphical style with never-before-seen story content and gameplay updates that includes a new, fully explorable underwater world and playable character in DRAGON QUEST II, among many other additions.
In related news DRAGON QUEST VII Reimagined arrives next year and is also already rated Steam Deck Playable.
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