In short, true time with it's relativistic property is bound to basically all 3 (at least and most likely more, but lets keep it simple) dimensions. Unifying space with time on both the subatomic and super-galactic levels therefore makes much more sense. 'Time' isn't actually something separate, it's not a separate spatial dimension and on itself is not even physical. Still it's evidentially essential.
It is simply no longer looked upon as a true 'fourth' dimension in the classical Euclidean space perception of time as just literally a ticking clock.

Ever since Einstein and friends managed to merge space and time into a single manifold with their theories, they've effectively simplified how to describe the workings of the universe in that area and made it much more unified. Basically that is what mathematics is for, a tool to create such manifolds. The reference to Minkowski was made to explain how spacetime is looked upon (in a mathematical sense) as the actual fourth dimension nowadays, instead of the older perception of 'time' (without being merged to 3D space) as a dimension with non-physical or non-spatial properties. In the Minkowski space, both timelike components and spatial components are mathematically described/explained.

I'm afraid you'll have to dive into and understand the theory of relativity for the Minkowski space to really make sense though. Much of it is simply a mathematical way of explaining how active time-related events make sense; causality relations described in a mathematical way.

Think about of describing how 'time makes a clock tick', yet then in any and all of the dimensional (spatial) directions.

This is all a significant difference compared to the older idea of 'time', even though it might not look like something too important in words. It's all about coherency and unification. Don't forget we aren't actually able to move through 'time', in whatever direction. One would experience the relativistic properties of spacetime under certain conditions, but one can not say that we posses the freedom of movement in a 'time dimension'. As such it's pretty odd to look upon time as a dimension. Spacetime makes much more sense.

Anyway, it's why one could basically argue that 'time' itself is no dimension at all.