Cheap option for recording HDMI output
An HDMI splitter is not what you need. You need either an HDMI capture card, or a standalone HDMI video recorder. The cheapest HDMI video recorder you're going to find is the Atomos Ninja Star, for $250 on B&amp;H: https://www.bhphotovideo.com/c/product/1285811-REG/atomos_atomnjs001_64_ninja_star_recorder_with.html

HDMI capture cards start around $130. Here is a good one from Blackmagic, for $137.50 on B&amp;H: https://www.bhphotovideo.com/c/product/964122-REG/blackmagic_design_decklink_mini_recorder.html