I imagine the situation is slightly different for a quadruped gait than for a biped like us... but even walking like this looks
profoundly weird if you see it in real life.
If someone glared at me across a rowdy bar, then walked towards me with a matched arm/leg gait, I would be rather more likely to burst out laughing than feel threatened.
I personally have no trouble noticing when this is wrong in drawings -- recently I saw that the RyanAir instructions on how to exit an aircraft get this wrong in a few places! -- but that's perhaps because when I was a child my siblings and I actually talked about this problem. E.g., if my little sister made this error in a drawing, my brother or I would point it out (not too unkindly, I hope) and demonstrate exactly what it looks like in real life to walk/run that way. I also remember just breaking into this kind of matched run spontaneously just to get a laugh. People who have never seen it before recognize instantly that something is dreadfully wrong, but it can take them a moment to figure out what's awry.
It's honestly hilarious to watch someone run this way -- I highly recommend trying it for entertainment purposes.
There's one exceptional circumstance when this is the natural gait: if you have a child sitting on each of your feet, and you are walking while dragging them along. THEN you need the extra lurch to help you keep moving.