The felt playing surface and padded armrest rail are the two things worth protecting on a poker table, since both scuff and dent more easily than the wood frame underneath. Blankets, not tape, are the rule around any felt surface.
Pro tip: Sprinkle a little talc-free fabric-safe powder on the felt before covering it if the table has been heavily used; it helps prevent the protective blanket from sticking to the fabric during the wrap.
Watch out: Never apply tape directly to felt or vinyl rail padding; the adhesive pulls fibers and leaves a residue that does not come out.