The Tux character in the attached blend does not play the walking animation. The parenting is set correctly (armature) and all modifiers have been removed.
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I can't open your file from here.
You need at least the armature modifier. You can easily get them by
Usually you need Vertex Groups set that match the names of the armature's bones.
ctrl+p Set Parent To \ Armature Deform \ With ... allows you to create such Vertex Groups.
I hope it helps