Your initial job, using programs like GSVA, is to do your best to ensure that all of your genes are in the correct annotation such that they can be used by the program. This will usually involve conversion from one annotation (e.g. Ensembl gene IDs) to another (e.g. HGNC symbols) using something like biomaRt. In reality, it is very rare that 100% of our genes can be used due to a whole variety of reasons. The effect of this is that statistical power may be lost, but I do not know of any studies that have attempted to quantify how much power is lost.
There is another important aspect to consider here: If the gene-sets in the program database are just comprised of protein coding genes, while your data has protein coding and non-coding genes, then, obviously, many will not match. However, you may still achieve 100% matching on protein coding genes alone.
The numbers going into each enrichment analysis should be reported in Supplementary Methods, but I am aware that they are usually not reported, which does not help.
Others may have other opinions.
Kevin