Does money earned from renting out an RV (through RVShare) count as a rental property income?

Yes, it is considered rental income from a business activity rather than rental income from real property.  Generally, you will report RV rental income on Schedule C Profit or Loss from Business.
 

Schedule C allows you to report your business's profits, whether you are selling homemade quilts at a craft fair or renting a guest house on your property or an RV.  You can deduct business expenses, like the cost of internet or phone, office supplies, travel cost, and the cost of your home office, provided all of these expenses relate directly to your business dealings.

To enter your RV income and expenses in TurboTax follow these steps:

1. Open or continue your return
2. Search for schedule c and click the Jump to link in the search results
3. Answer Yes to Did you have any self-employment income or expenses? If you've already entered self-employment work and need to enter more, select Add another line of work
4. Follow the on-screen instructions to enter your self-employment information

This TurboTax link Where do I enter Schedule C? has information you may find useful.

Schedule E is specifically for reporting rental income or losses pursuant to real estate. Schedule E requests information like the physical address of each property you rent out, the fair rental days versus personal use days for each, the type of property for each, and the rents and royalties received. You will also be given the opportunity to deduct all of your expenses from your income.