Using reference PCB trace antennas without tuning them
This antenna is fairly broad band and omni-directional, so I would expect it to be relatively insensitive to normal manufacturing variation.  Also, as it describes, it doesn't use a bottom side ground plane, which makes it less sensitive to the thickness and dielectric constant of the PCB.

There are ways to tune without a network analyzer, but it really depends on what tools you do have.  This antenna is not really designed for tunability   anyway, so I don't know what you would do even if you had a network analyzer, other than maybe rescale the drawing slightly to shift the peak frequency.  I don't really think you are going to have a problem just making this as-is.