Totally normal sighthound play behaviour. Noisy, fast, argy-bargy. They live to run/chase and don't quite get it that other breeds might not feel the same way.
My older Lurcher plays well with other breeds, because he was raised from a pup with a Soft Coated Wheaten and a Belgian Shepherd x Border Collie and learned his playskills from them. He also has a good recall, so I can pick and choose who he plays with anyway, that way I can check with the other owner before I let him go.
My younger lad is a much more natural/instinctive Lurcher type and he will play just like your girl if allowed, only he's been known to remove clumps of fur from my older lads rump when he was younger and more OTT. I don't know his background as he was dumped at birth, but I suspect he may have been from working lines and he does the other ill-mannered Lurcher thing of nipping necks and tails as the other dog runs as well. Many Lurcher owners muzzle their dogs for free-running for this reason. They don't intend to injure, it's purely play, but with sighthound thin-skin it's a recipe for lots of vet visits when they play together.
I don't allow him off-lead with other dogs for this very reason, but he's done a good job of reminding my older boy that he's actually a Lurcher too - so they have a blast together instead. It's interesting that, having been introduced to Lurcher play by Pip, our older lad still plays nicely with other dogs, so in his case it's definitely a case of nuture over nature - although he is much more of a mixed breed than Pip, with a good dollop of Collie in there as well, so not as sighthoundy to begin with.
Their instinctive desire to chase is triggered when they see a fast moving animal (note I said chase, not kill as some people would have you believe) and it really is very hard for them to resist. You can teach them not to go - although it's not easy.
The one thing I have done is work extremely hard on Pip's recall, so I can call him back mid-flight if he does decide he'd like to have a run with someone else. I use a whistle for consistency and also because whistles seem to get through to a chasing sighthound brain much more easily than vocal cues. He stayed on a long-line until I was sure he would come back, even when really tempted to run and was really good until a few months ago, when puberty hit, then we went back to basics and did it all over again! 
Generally speaking I wouldn't let him off in a typical dog-walking park where there are lots of other dogs off-lead. He would stay on a long-line in that situation and does socialise with other dogs, but only on the lead. We generally walk up to the fields at a quiet time of day for mine to have their loopy lurcher blasts and I agree with CMOT, that a Lurcher pal would really help your girl to burn off her need to run. I know my boy won't run unless he has someone to run with, so wouldn't get enough exercise without our older boy to play with.
Are you a member of Lurcher Link? If not I would advise joining. You can then post asking for advice from lots of very experienced Lurcher owners and also ask if there's anyone nearby that would like to walk with you occasionally.