Our Last Braves Game

[busker]

I don’t know whether there’s a contextual joke in the (Atlanta) Braves vs South Decatur, and whether the latter hosts a rival American football or baseball club.
Can’t understand the first two lines either - what ruin, and what crack? Why mention the normally expected two way loss?

Why would you need to know “what ruin?” and “what crack?” to understand this? - because otherwise they're filler words. Filler words cheat the reader.

I’m sure you do understand it, but you just don’t know what specific ruin or what specific crack… because I haven’t put those bits in. I leave it up to you, dear reader, to imagine the ruin and imagine the crack and imagine what those words might mean in relation to the theme of the poem—they may even mean more than one thing at a time! - no, the reader is not sufficiently invested in the poem in L1 and L2 to make the mental effort. Because these are filler words

As for the second, in terms of relationships, I’m not sure it is an expected two-way loss. Often, someone gets dumped, and they are the loser. In fact, “it’s their loss” is a common refrain of the friend or relative of the dumped. 
it comes across as a lazy continuation of 'I lost my girl', but that's ok

Because to lose something implies you cared to have it. You seldom really lose what you throw away. So, I thought I would balance the equation like that to show the insecurity of the author. 
None of that 'balancing' comes across in the poem.

Also, it implies she's not dead (this isn't a dead girlfriend poem)... and, lastly, I think it’s funny humorous word play.
it most assuredly is not word play

And no, there is no contextual joke in the title. 
my bad, I assumed there was cleverness.

In fact, it's about as straight forward a poem as a poem can be, so I'm a little surprised you're struggling with it. 
'struggling' overestimates the merits of the poem. I'd say that it's a piece of doggerel and I was expecting something a little cleverer.