Gave your ZvP game a watch, some comments:
Opening: You kind of pause at 13 food without producing/doing anything, going up to around 400 minerals, I think you were controlling your drone scout and forgot to produce while that was happening. Most openings in ZvP, you should produce drones up until 14 or 15 food and then build a pool, then expand a little afterwards.
General Mechanics: Your macro is probably the biggest area that needs work here, which makes sense since you're coming from a MOBA background. Zerg centers around powering your economy with drone and larvae counts.
-Sometimes it's a general issue of being inefficient and not producing more workers or units when you have both the money and the larvae (eg: the issue with your opening). You can work on this by practicing "cycling" - it's a concept that Day9 introduces in one of his introduction to SC2 videos (don't remember which episode, if I remember I'll link it later), but it essentially means that you should try to be mindful of all the things you need to constantly be doing and "cycle" through them constantly via things like hotkeys. So, to avoid forgetting drone production while controlling a scout, you might "cycle" through your hatchery hotkey and your drone hotkey jumping back and forth between the two so that you remember to build drones ASAP when new larvae are available while at the same time making sure your drone is scouting.
-Injects. Injects is key for zerg macro, and throughout that game, I counted maybe five injects you did total in a 19 minute game. I recommend hotkeying all of your queens to include them in your cycle, and there are a number of little techniques that people use to do injections at all your hatcheries extremely quickly and efficiently. Here's the most recent one.
More Specific Issues:
-Why you lost: Primary factor for the loss was that you didn't have enough gas. You were banking huuuge amounts of minerals: by 9:30 you have over 2800 minerals, and by the end of the game you had around 15000 minerals. The whole game, you only had one geyser mining - you built two more through the course of the game, but never put drones in them to mine, and even ordered a drone off the one extractor you had so that you only had 2/3 drones mining one extractor out of 3 bases. Meant that you didn't have gas to build corrupters, infestors, or hydras, all answers against the protoss' air units. Timings on when you should get gas vary depending upon what you want to do/what you need to do in response to what your opponent is doing, but as a general rule, definitely get more gas when you're running more than a 3:1 ratio of minerals to gas. But because you were so gas starved, you could only make zerglings, which can't attack air and aren't good against zealots unless you have enough of them, but because you didn't have enough injects, you didn't have enough larvae to really build enough lings to beat the zealots.
Another recommendation: sometimes it's hard to get all those injects, which is understandable. Another way to respond to having such a high mineral bank is to build an extra hatchery or two in your bases, what we call "macro hatcheries." These are solely used for their additional larvae, to help you produce additional units. And if you have, say, 10k minerals, you can definitely spare the 300 minerals for more larvae.
-Army Composition. Banelings are fun, but they can't shoot up, so you didn't have anything to kill the air units. Furthermore, while you did kill his initial batch of zealots with banelings, you didn't replace those banelings with enough units, so the follow up wave of zealots also finished you. First, in general, roaches would probably be a better bet against zealots. Your roach warren was extremely late (~16:00) and you didn't build any. Hydras also could have taken care of the air units, and you had a hydra den relatively early that game compared to the rest of things that you got, but you only started production when the protoss was already pushing in and by then it was too late/you didn't have enough gas to make a sizable enough force because of the aforementioned gas issue.
-Tech. Get upgrades for your units! You didn't build/use any evolution chambers that game (and not having gas would also limit you in this area).
Hope the comments help!
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