Severance taxes (Texas or elsewhere) are not considered a royalty burden (meaning, deduction from royalty ownership). They are a deduction from revenue share received by the payee (royalty owner). The royalty paid (“revenue”) is a gross fraction or percentage of total sales, stated directly in the oil & gas lease in the royalty clause.
Your question is a bit unclear to me, though. Is the “offer for purchase” to buy your mineral rights, or is it an offer to purchase an oil & gas lease from you? There are two possible answers, depending on which scenario.
If the offer is to buy your mineral rights (and not take a lease from you), the language would be referring to any non-participating royalty interests owned by third parties that you might not know about, who would be entitled to part of the lease royalty stated in any future lease. The offer is saying that the amount of money they are offering you is based on them being able to negotiate a 1/4 royalty lease in the future, and be paid all of that 1/4 royalty, none of it to be paid to NPRI owners (non-participating royalty interest owners).
On the other hand, if the offer is for you to sign an oil & gas lease (not to sign a deed selling your rights), the language would be protection language for the Lessee. The oil and gas lease will state 1/4 royalty in it, but the company making this offer wants to make sure you understand that you will not receive all of that 1/4 royalty as revenues if you have NPRIs burdening your royalty rights. The NPRI revenue share(s) would get paid to those other owners and you would receive only the balance.