Streaming is best served with numerous cores/threads, whereas gaming benefits more from higher speed, efficient cores.
The Xeon turkey linked is a great balance. Quad Core + HT (8threads) is essentially an i7, without the iGPU for a lesser cost. It fits within budgets that would only allow a Quad core i5 if viewing the standard i3/i5/i7 range.
Usually, you go to higher numbers of cores and either the speed per core reduces significantly, or the overall cost skyrockets. The Xeon listed is a good balance of cores vs clock speed vs price.
For example:
Xeon E5-2650 is an 8 core + HT option, somewhat reasonably priced ($600ish) but clocked at 2.0GHz.
To go with a higher core option, with somewhat reasonable speeds, let's look at the Xeon E5-2697. A 12 core + HT option, clocked at a decent 2.7GHz (turbo'ing to 3.5GHz), but comes is priced at $2,500
Both would be great for streaming (multiple cores), although overkill. For gaming though, they'd be pretty poor performers (relatively speaking) due to their lower clock speeds.
One of the best options for these needs, at a (relatively) decent price point would be an i7-5820k + X99 motherboard. 6 core + HT @ 3.3GHz.
You could give her this i7 & pair it with the 290x you already have.......if you're planning to upgrade anyway. It can be done right around a $1,000 budget (since the GPU cost is removed) but, depending what setup you have, you might want to keep it for yourself! haha.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i7-5820K 3.3GHz 6-Core Processor ($351.98 @ Newegg)
CPU Cooler: Corsair H110i GTX 104.7 CFM Liquid CPU Cooler ($99.99 @ Newegg)
Motherboard: Gigabyte GA-X99-SLI ATX LGA2011-3 Motherboard ($133.98 @ Newegg)
Memory: Team Delta 16GB (2 x 8GB) DDR4-2400 Memory ($57.99 @ Newegg)
Storage: Samsung 850 EVO 250GB M.2-2280 Solid State Drive ($79.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($45.89 @ OutletPC)
Case: NZXT S340 (Black) ATX Mid Tower Case ($63.99 @ SuperBiiz)
Power Supply: EVGA 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($48.99 @ NCIX US)
Operating System: Microsoft Windows 10 Home OEM (64-bit) ($86.95 @ OutletPC)
Total: $969.75
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-03-22 18:02 EDT-0400