I have this setup for my outdoor speakers:
Chromecast > HDMI audio extractor > Amplifier > Bose outdoor speakers
Works great and was fairly cheap. I can control it from my phone or google homes. Biggest downside is that the AMP volume is not remotely controllable.
https://www.amazon.com/Lepy-LP-2020A-Digital-Amplifier-Stereo/dp/B00C2P61FO
Got this for mine. Works great. Lepy LP-2020A Hi-Fi Digital Amplifier, Mini Stereo Audio Amplifier with Power Supply Black US https://www.amazon.com/dp/B00C2P61FO/ref=cm_sw_r_cp_api_i_ONuyEbV77YNCX
Those speakers aren't powered are they? That Fiio isn't going to get anywhere near the amount of power that you're going to need to get much out of those speakers.
A basic amplifier like the Lepy LP-2020A would get you a lot closer to the power demands that you need.
For a bit more I like the SMSL SA50. It's nicer to use and has a bit more power than the Lepy unit.
For a basic explanation of why that FiiO isn't going to get there... it pushes a maximum of 78mW (.078 watts), your speakers will need more power than that...to get to 87dB at 1 meter you'll need 1 watt.