Reddit reviews Gap Stopper Pro - 21" Clear, Professional Grade, FDA Heavy 8.6 oz Silicone, Set of 2, Covers Gap between Stove & Countertops
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Professional Grade, Heavy 8.6 oz SiliconePrevents food from falling in to the hard-to-clean gaps between your stove and countertopsSeal the gaps between even and uneven surfacesT-shape and the silicone material help keeps seal in placeEasy to install and easy to clean
Since you're renting, I would get something like this http://www.amazon.com/Gap-Stopper-Premium-Silicone-Covers/dp/B018T5D4QO/ref=sr_1_6?s=hi&ie=UTF8&qid=1458121325&sr=1-6&keywords=silicone+gap+cover
And use the L shape.
Get regular silicone and stick a few of them together end to end (probably use scraps of it and act as extra bonding surface like this -=-) until it's long enough or see if you can find something in longer lengths. Glue the short side facing the water to the floor with more silicone and that should act as a dam. When you leave you can just peel it up and scrape off the silicone residue.