No, you do NOT need Xbox Live Gold for Single Player.
What Requires Gold (Xbox 360 Legacy Policy):
What Works OFFLINE (Silver/Free):
Important Note: Minecraft: Xbox 360 Edition (Legacy Console Edition) stopped receiving updates in 2019 (Update Aquatic was last). The modern Minecraft (Bedrock) is not on Xbox 360. On Xbox One/Series, **Xbox Live Gold is no longer required for Free-to-Play games** (including Minecraft Bedrock multiplayer), but the 360 edition still follows the old policy.