Last time I was in Bellview was 1978.
The Avenue was almost the 1st building on Fairfield in Bellview. Right after the flood wall if I remember. The building in the picture is not even close to what I remember. There was a parking lot on the left of the Avenue that sloped down to the river. The Avenue had a good sized window in the front.
Besides the sign on this building says Avenel Social Club.
Now that I showed off my memory:

Barneys was at 713 Fairfield. 6 blocks closer to Dayton. The Avenel looks like it might have been a garage at one time. 6 blocks would be pretty close to Dayton.
My grandmother who made it to 111 years owned a small grocery store in Dayton.
I have been in The Avenue many times but never while they had gambling. I don't even remember Barneys but it looks like the bar my uncle used to send me to, to get a quart of beer for him, back in the 40's & 50's.