The musicianship displayed on this recording is of a very high order, and the sonics are very good. This is a performance that creates a new Brahms First for the modern world, a Brahms that speaks to us.
This should not however be confused with Brahms as Brahms would have heard it. Brahms died in 1897, the phonograph was invented in 1877, and flat disc records in 1881. We have an ample auditory record of what musicians of Brahms' time sounded like, and this is not even close.
We have recordings of Joseph Joachim (the violinist for whom Brahms wrote his concerto) as well as other violinists of Brahms' time, and clearly vibrato and a lot of portamento were used. Joachim's vibrato is spare, but to use none at all, and no portamento, is not in keeping with the known performance practices of Brahms' time.
Beyond those primitive early recordings, some musicians who knew Brahms, conducted for Brahms, and heard Brahms conduct lived well into the mid-twentieth century, when electric recording techniques were available.
If you are interested in hearing something close to what Brahms must have heard, look into Felix Weingartner's recordings from the 1930's. Weingartner was in his mid-thirties when Brahms died; Brahms heard him conduct his Second Symphony, and liked what he heard. Weingartner also heard Brahms conduct his Third and Fourth symphonies.
The standards of orchestral playing were not as high in the 1930's as they are today, and there are imperfections, but this is the closest to "authentic" Brahms as it is possible for us to have. The recordings themselves were made using an electrical process with microphones, and are not primitive.