I don't see anything unusual here. To explore the data values that are going in to the linear fit, I added a layer with the original values
and used the Inspector to look at example pixel values (select the Inspector tab next to Console and then click on a point on the map)
Layer 1: Image (5 bands)
Slope of linear fit: Image (2 bands)
From this we can see that the slope is not an integer. You were probably looking at the histogram chart's values — a histogram creates "buckets" of some width to count similar values, and in this case chooses integer representative values for those buckets.
The large slope value is not unreasonable, either: just look at the numbers. If we compare the end points it goes from 1400 to 1148, a difference of 242 on the y axis with a difference of 4 on the x axis, or a slope of 242/4 = 60.5 if we "linear fit" only those two points. You could take that number sequence and run the fit using another tool or on paper and I expect you'll get the same answer.
(You didn't ask, but the offset value is large because the data has a large offset in the x-axis: it goes from 2006 to 2010, not around zero! So we can generally expect the offset to be of the magnitude 2008 times the slope — 2008 × 84.75 = 170178, there we go.)