乒 and 乓 have onomatopoeic use for sudden noise from a gun or similar. Their resemblance with an actual pingpong table is coincidental, and the characters were chosen for the sound playing the game makes.
See https://zh.wikipedia.org/zh-cn/乒乓球 for the history.
Both characters are used individually, but do not form any other words than 乒乓 and related terms. They derive from 兵 (bīng, soldier).
Edit: Expanding a bit, because these characters are a bit of interest. They seem to appear during Ming in the 16th century, with the vernacular literature of the time. Some examples:
西游记 / Journey to the West (Ming, 1580): 如此二三日，又听得后宰门乒乓乒乓，砖瓦乱响。
封神演义 / Creation of the gods (Ming, 1560): 乒乒乓乓，如同阵前炮响；轰轰烈烈，却似锣鼓齐鸣。
儒林外史 / Rulin waishi / Unofficial world history (Qing, 1750): 忽然乒乓一声响，屋梁上掉下一件东西来；不左不右，不上不下，端端正正掉在燕窝碗里，将碗打翻。
Some sources tell that 乒 is a hand holding a pickax, but late characters are rarely if ever ideographic in nature. More likely, some creative author used 兵 to coin a new set of onomatopoetic characters. 乒乒乓乓 has so become a proverb from the Ming era romance literature.