I the article was written in 1960. Art Gran's Gunks guide used the YDS in 1964. The YDS was around at the time of the article, but it is reasonable to assume it wasn't something Fritz would use. The Appies had their own system (see chart below), there was an alphabetic grade system in use by IOCA, and the Vulgarians were using the YDS, because they were the only group in contact with the California climbers.
So definitely not the YDS system, but rather a version of the European alpine grades, I think not all that different from the current UIAA grades, expressed in roman numerals in the left-hand chart below.
The right-hand chart, which is kinda fuzzy, has a comparison of "AMC grades" in the Gunks to YDS grades at Tahquitz, including example climbs that are supposed to be comparable (but are not; many of the gunks climbs are notably harder then their purported Tahquitz equivalents). Those AMC grades are derived from the European grading used by Hans and Fritz and are a little softer, in YDS terms, than the UIAA versions. The chart comes from an article in Summit magazine promoting the National Climbing Classification System, a good idea that was ahead of its time and never caught on. See http://www.supertopo.com/climbers-forum/...ger-Summit-1963
I suspect Fritz's grading was closer to the current UIAA scale. That being the case, the "grade 4's" Fritz referred to would be 5.4-5.5 and the "grade 5's" would be 5.7, with 5.8 for the "upper 5's" he mentions. I think this fits pretty well with our modern grading of the climbs he mentions, with the exception of the Old Route, whose modern grading of 5.5 would be (IV-IV+), which does not agree with Fritz's grade 5, especially since Fritz apparently stood on a piton somewhere. This does lend credence to my observation in an earlier post about the possible undergrading of the Old Route.
The AMC chart does suggest how Old Route got to be 5.5, because in that chart AMC 5 corresponds to 5.5-5.6.