Sure ..
after the land parcels and ennumeration scheme had already been laid down .. and not limited to rail grants - there was a general US pattern of checkerboarding all land grants to disperse development.
The foundational aspect to the question posed is that land was gridded in abstract from afar before any aportions were made, a secondary aspect was that in some regions large tracts of those squares were initially granted to various railroads on an "every second large chunk" basis, another aspect was that in the days of open cattle grazing early land cattle barons realised they didn't have to own land to graze on it and they could control access to unowned land by only paying for surrounding land or for "chokepoint" land in rough terrain.
A 'final' aspect to the story is the creation of the US National Parks movement which started a wave of "freezing" as yet unsold land as permanently held as not for private use.
A key point is that the Land Grant Act of 1850 granted checkerbordered land to railroad companies within at most 50 miles of planned rail routes .. however that practice wasn't limited to rail grants - Tribal lands were also checkerboarded by the Dawes Act and public land was released on a checkerboard basis.
You can see the checkerboard ownership even in early cattle country that had no history of railroad grants - the large squares were the unit of sale and typically the early sales were for homesteads in the midst of unclaimed land with the next sale not being "right next door" but for another homestead block in the midst of unclaimed land.
It's the appeal of owning your house, shed, assets, yards, etc. while not having to pay to own the land your cattle are moved through for seasonal pastures.
Eventally all land would presumably have been purchased .. but the National Parks started freeing things up.
There's more on this (but not the complete picture) in:
https://en.wikipedia.org/wiki/Checkerboarding_(land)