License to Use Products. Following payment of the applicable fees for a Product, you will have the non-exclusive right, for the period selected by you in the case of a purchase for a rental period, and in other cases for as long as Google and the applicable copyright holder have rights to provide you that Product, to download or stream, in each case, solely as expressly permitted by Google via the Play user interface and subject to the restrictions set forth in these Terms and associated policies, copies of the applicable Product to your Devices, and to view, use, and display the Product on your Devices or as otherwise authorized by Google as part of the Service for your personal, non-commercial use only. All rights, title and interest in Google Play and Products not expressly granted to you in these Terms are reserved by Google and its licensors.
Am I missing something or does that mean a school, particular a private school, could not use the Play store at all? What legal avenues does that leave for us to purchase apps?
It seems bizarre for Google to be barring businesses from using the store. The Apple App store has terms specifically allowing use by businesses. Google Play for Education seems to be coming but not actually available yet, and it is not clear to me whether it will be available in the UK straight away.
Education, even private education, is often counted separately from commercial use. Schools, even private ones, are not profit making businesses. Their entire income is invested in the education of children whether that is from the government or derived from fees. Private schools are charities for this reason.
However private non-commercial is usually assumed to include schools unless it says otherwise.
Hopefully someone else will have found something to help you in the play store T&Cs. Summoning edugeek's legal eagle @GrumbleDook as he may have already come across this one in particular in his previous role.
Google is pretty clear about what is included for educational use in their products, through what they deliver for Google Apps for Education. This seems to be one of the drivers for the inclusion of the Play store into this set.
Many companies, such as Google, turn a blind eye to the use of certain personal products when it comes to education ... and you even find their evangelists promoting the use of personal products ... but the company will tend to come back and quote you the T&Cs if you ask them a direct question about using it ... rather say an outright yes or no.
A good number of private / independent schools are within a charitable trust, so many will argue that this sets them outside of the commercial sector, and this would be a healthy arguing point if challenged.
Google, like Apple, are doing a fair bit of promoting sets of their products as part of the delivery of personal devices. If you are going down a 1:1 scheme this fits in well, but it makes it hard to manage on class sets of machines using schools generated and controlled accounts.
Ok, I know ... not a clear yes or no, but I'll go and ask a friendly Google Trainer (there are a few who lurk on here) to see if there is a better answer.