The mishna teaches what the qualifications are for a kosher animal, bird, fish and chagav. The Rambam in sefer hamitzvos (149-152) counts each of them as a separate positive mitzvah. Although the Ramban in his comments on the mitzvos doesn't write anything, in the sherashim of sefer hamitzvos (shoresh 6) he articulates his opinion that none of these deserve to be counted as a מצות עשה. The rationale of the Ramban is quite logical. There is no obligation to eat these items at all, and therefore the mitzvah to check the simanim is essentially teaching what is allowed and not allowed to be eaten, without any command. The Ramban does consider the positive mitzvah to be an additional violation for one who would eat a non-kosher animal in which these simanim are absent, but does not consider it a mitzvas aseh to actually check the simanim. The Ramban and Behag (quoted by ramban) seem to differ whether the eating of a non-kosher animal should even be counted as a separate aseh, but they both agree that the checking for simanim isn't worthy of being counted as an aseh.
By looking more carefully at the language of the Rambam in sefer hamitzvos (149) we get a better appreciation as to how the Rambam considers these to be positive mitzvos. The Rambam writes
והענין במצוה זו מה שזכרתי לך, והוא שאנו מצווין לבדוק אלו הסימנים בכל בהמה וחיה ואז מותר לאכלן, והדין הזה הוא המצוה
The Rambam seems to understand that the nature of this mitzvah is not an obligation to check the simanim. Rather, the Rambam seems to hold that the very nature of the din which distinguished between kosher and non-kosher, is worthy of counting as an independent mitzvah. This doesn't mean that by checking for simanim one fulfills a mitzvah aseh, but rather the existence of dinim that are necessary to abide by in order to achieve a desired result, qualifies as a mitzvah. A similar logic would have to be applied to explain why the Rambam counts shechita (146) as a mitzvas aseh - although there is no obligation to eat meat, the dinim of shechita that one must abide by to render the animal kosher, qualifies as a mitzvas aseh. The mitzvah of writing a gett would be similar, not an obligation, rather a set of dinim that one must abide by if they want to achieve a particular result. However, the Megilas Esther and Kin'as Sofrim (two classic commentaries on sefer hamitzvos - shoresh 6) both seem to take the approach that the act of checking according to the Rambam is a fulfillment of a positive mitzvah. The Kinas Sofrim explains that if one were to eat an animal without determining that it is kosher and only after consumption realizing that it was indeed kosher, they would be in violation of this mitzvah aseh. The same should be true if one were to eat in a restaurant without verifying that it is kosher and only afterward finding out that it was indeed kosher - the laxity in failing to examine prior to eating is a violation of the mitzvas aseh. According to this approach, the failure to pre-examine the kashrus status prior to consumption is very different than other issurim. If one were lax about other prohibitions and not pay close attention to whether it is actually permitted, and then find out it was permitted, it would fall under the category of מכוין לאכול בשר חזיר ועלה בידו בשר טלה, which requires teshuva but is not a violation. However, according to the Rambam even the laxity in determining the kashrus status of an item would be a specific violation of a mitzvas aseh. The statement of chazal that one needs to do teshuva when they try to eat pork and end up eating kosher meat, is actually a strong question to undermine the kin'as sofrim's approach to the Rambam. Why would chazal just say that you need teshuva for the intent of the aveira, you should need teshuva for violating the aseh and not inspecting the food before consumption? It therefore seems to me that the Rambam considers even a din of inspecting to be counted as a mitzvah even though there is no obligation to do so.
As an aside, the language of the Rambam at the beginning of ma'achalos ha'asuros contradicts his language in sefer ha'mitzvos. In the mishne torah the rambam uses the term לידע, implying that the nature of the mitzvah is to learn and be knowledgeable to be able to discern between kosher and treif, whereas in sefer hamitzvos he uses the term לבדוק implying that the nature of the mitzvah is to actually examine?