Spark Edition is likely a version of Personal Edition or Free Edition, rebranded to fit the Lightning theme (a Spark is smaller bit of electricity than Lightning). These orgs were extremely limited in nature, allowing minimal customization and minimal CRM features (really, just Accounts and Contacts). These types of orgs were common circa 2009, but were discontinued at some point. If I saw the Company Information page (including the Features and Limits section), I could identify which one it is specifically. The point is, you can only install AppExchange packages that don't exceed the limits of the org.
There's two types of packages on the AppExchange: those that ignore limits, and those that don't. You can install the former in any org that has all the features that the package depends on. You can install the latter only on larger orgs that have enough capacity to support installing the package. This means that it's possible to install a package with 100 custom objects, assuming it passed the security review, yet not be able to install a package with 1 custom object, if you were already at your limit.
The only option you have would be to contact Sales and upgrade the current edition. The only option the managed package provider would have is to complete a security review, thus exempting their package from the normal org limits. Other than that, you will not be able to install this package in to this org. In simple terms, someone is going to have to pay money in order to get this package in to this org.