Without a doubt, play will be adversely impacted by placing it in a room that narrow. At a minimum you need 64 inches of clearance on all sides to accommodate a standard 58 inch cue without an impeded backswing. With the dimensions of your room, you will definitely need a short cue for when balls are close to the long rails. Whether or not that is a deal breaker for you is up to your preferences and how serious of a player you are.
As for your comments on price, I wouldn't be so hasty to think that's a great deal. There are maybe 3 models of pool table that have any sort of value on the used market. I believe the model you mentioned is a 'furniture table' and if so, does not fall into this category. If you browse facebook marketplace you'll see that the used market is full of similar tables. Despite their high initial new price, they're worth maybe a few hundred dollars at most once used. Many can be found for free due to the amount of effort that goes into tearing down/moving pool tables. I bet you're looking at another $500-750 to get someone to move that table, reassemble/level at your house, and replace the cloth. So all of the sudden that $650 table is looking a lot more like a $1,000+ one. If you're absolutely set on that table, I'd offer the seller a couple hundred bucks and see what they say. Pool tables are not an easy item to sell and there are a ton of them on the market so you certainly have leverage in a negotiation.
