Likewise, I don't think there is such a gap in Bigglesworth's AoE for Kazuma's supernatural luck to let him evade it if he's in range & can't move out of range in time.
I'm not sure what use Teleportation is for Kazuma is if he teleports himself, unless he can Teleport back to Central Park, but if I understand the thread right, he needs a waypoint to teleport himself or something else somewhere, right?
& while the quote does seem to indicate that Kazuma can teleport other beings without touch, it seems to have gone off shortly before the sword reached his body, implying close range. Not to mention, a cat is much smaller than a human. An average of 24 cm vs a grown man's average 170 cm or so; Less than a 7th of the height. Lengthwise, they're about 46 cm in body length + 30 cm tail. Not accounting for tail movement, that's over 2.2 times less than a person's height.
So if Kazuma has to AIM his teleport spell (For example, pointing his hand at the cat.), he has a much smaller target, & an aggressive cat like Bigglesworth (Who, thanks to Prior Knowledge, will presumably have the sense to dodge.) has much more room to zig zag, unlike a swordsman charging straight to impale him, which is what Kazuma DOES have experience using teleport offensively on. As opposed to a much smaller, dodgier target he probably can't even see well in the grass, & may not have in his field of view unless he's bent over or such.