Is this being a swinger?

is it considered being a swinger when the husband and wife are dating the same girl??

This is off Dictonary.com

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American Heritage Dictionary - Cite This Source - Share This swing·er (swĭng'ər) Pronunciation Key
n.
One that swings: a good swinger of baseball bats.
Slang
A person who actively seeks excitement and moves with the latest trends.
A person who engages freely in promiscuous sex.
A member of a couple, especially a married couple, who exchanges sexual partners.

So your answer is Yes!

It really just depends. Do both the husband and wife know they are dating the same girl? and does she know she is dating both of them? Are they all open with this? This could be simply considered an Open Marriage - not swinging. Now, if the three of them did the wild thing together (all three of them, commonly known as a three-some), then they would be more pragmatically considered to be swingers.