The poem is a short, unsettling picture of a marriage that has slipped into performance. The speaker and his wife "play with puppets," a phrase that suggests they are no longer dealing with each other directly but acting out roles, letting stand-ins speak for them. The title, "Games," points the same way: what looks like play may be a way of hiding.
The middle lines say it plainly. The more they play, the more love "begins to grow stale." Pretending doesn't keep the feeling alive; it seems to wear it down.
The last image is the strangest. The speaker takes "the lark / that pretends to sing" from his wife's mouth. A lark is a bird of real, spontaneous song, so a pretend one feels hollow. Taking it out could be an act of honesty, ending the pretence, or a small act of loss, since he removes even the imitation of her voice. The mood is quiet, sad, and a little eerie, with the speaker seeming both weary and clear-eyed.